{ "schema_version": "0.1.0", "title": "Spectral-branding corpus map — papers, terms, claims navigation graph", "description": "A generated graph of the open corpus for seed->scope expansion: from a seed of 1-2 papers, widen to every paper bearing on a task via shared terms and corpus-internal citations. Navigation only; claim/method text lives in consult.json (L1/L2) and each paper's spine.", "canonical_url": "https://github.com/spectralbranding/corpus-guide", "generated": "Generated projection of the open spectral-branding corpus substrate (papers <-> terms <-> claims graph). Do not hand-edit; regenerated from source.", "how_to_expand": [ "1. Start from your seed paper key(s) in papers[].", "2. Read each seed's terms{owns,imports,refines}.", "3. For each term, look it up in terms[] and follow papers{owns,imports,refines} to every other paper that uses it — those are in-scope.", "4. Also union citation_edges where from/to is a seed (who cites / is cited by it).", "5. Ground the answer in the widened set; state any paper you could not resolve." ], "counts": { "papers": 49, "terms": 206, "citation_edges": 396 }, "papers": [ { "key": "2026a", "title": "Spectral Brand Theory: A Computational Framework for Multi-Dimensional Brand Perception", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.18945912", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/spectral-brand-theory", "thesis": "Brand perception is irreducibly observer-dependent: there is no single brand-in-itself with properties, only a shared signal environment and heterogeneous observers who each collapse it into a structurally different conviction. Spectral Brand Theory decomposes brand signals across eight perceptual dimensions (Semiotic, Narrative, Ideological, Experiential, Social, Economic, Cultural, Temporal), defines each observer cohort by a formal spectral profile (spectrum, weights, tolerances, priors, identity gate, encounter mode), and models perception as a pipeline — signal emission to observer filtering to probabilistic perception-cloud formation to threshold-based conviction collapse to re-collapse on new evidence. Single-score brand measurement (NPS, equity indices) collapses this multi-dimensional, observer-mediated structure and destroys the very information that explains why observers form irreconcilable perceptions of the same brand. SBT formalizes the heterogeneous observer that customer-based brand equity theory acknowledged but never parameterized, yields five testable structural propositions, and is computationally implementable as a structured LLM prompt sequence. An illustrative five-brand proof-of-concept surfaces four candidate mechanisms (structural absence, a five-type coherence taxonomy, asymmetric conviction resilience, and brand-power/brand-health independence); these are candidates for empirical investigation, not validated findings, and human-subject validation is the priority next step.", "n_prop_claims": 15, "terms": { "owns": [ "brand-conviction", "brand-fact", "cloud-valence", "cohort", "d-a-ratio", "observer-spectral-profile", "perception-cloud", "re-collapse", "spectral-brand-theory", "spectral-dimensions", "structural-absence" ], "imports": [], "refines": [] } }, { "key": "2026aa", "title": "Optimal Response Formats for AI Brand Perception Measurement: Evidence for a J-Shaped Rate-Distortion Curve", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19528833", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r19-rate-distortion", "thesis": "Applying Shannon rate-distortion theory to AI brand-perception measurement, the response format constrains an LLM encoder's output alphabet (rate) and the total-variation distance from a canonical eight-dimensional brand profile is the distortion. Across 17 architectures from distinct training lineages, the empirical rate-distortion curve is J-shaped rather than monotonically decreasing: minimum distortion occurs at an intermediate bounded format (1-5 ordinal scale, ~19 bits) rather than at the highest-rate format (100-point allocation, ~26 bits), a 49.4% mean-distortion reduction (.172 ->.087). The departure from classical monotonic R(D) is mechanistic, not mathematical: the encoder is an active agent whose training-corpus priors express most freely under unconstrained high-rate formats and are suppressed by bounded quantization. All 17 architectures trace essentially the same curve (codebook convergence), prescribing 1-5 ordinal scales as the optimal elicitation instrument for recovering brand perception profiles from LLMs.", "n_prop_claims": 9, "terms": { "owns": [], "imports": [ "cohort", "observer-spectral-profile", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026ac", "title": "Spectral Immunity: Why Brand Portfolio Interference Disappears for AI Observers", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19765401", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r21-spectral-immunity", "thesis": "Brand portfolio theory predicts perceptual interference between commonly owned brands whenever an observer's awareness gate is open. Large language models, whose training data permanently saturate that gate, are a critical test case. Formalizing spectral interference across eight perception dimensions and testing three propositions in a fully crossed experiment (13 LLMs, 7 training traditions, 40 brands, 7 portfolio archetypes, 4 prompt modalities; N = 9,925), the paper finds near-zero portfolio-induced change (mean |ΔDCI| =.26; TOST equivalence for 18/20 brands;.1% of DCI variance from portfolio framing versus 37.4% from brand identity). The sole exception is a reverse-aspiration structure (Geely Auto) under multi-turn conversation (d = -1.11), where extended context converts coordination information into output inference. This resolves the awareness-gate paradox: awareness is necessary but not sufficient; a perception channel with adequate bandwidth to encode portfolio context — rooted in rate-distortion theory and rational inattention — is also required. General-purpose LLMs are rationally inattentive to organizational-coordination (DO-layer) signals because these contribute negligibly to output-fidelity (WHAT-layer) reconstruction, so portfolio architecture becomes strategically invisible in AI-mediated channels.", "n_prop_claims": 7, "terms": { "owns": [ "spectral-immunity", "spectral-interference" ], "imports": [ "brand-conviction", "cohort", "observer-spectral-profile", "perception-cloud", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026ad", "title": "Restoring Perceptual Separability After Coherence Shocks: A μ > λ Threshold Inequality in Brand Perception", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19778549", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r22-spectral-gap-restoration", "thesis": "Brands facing coherence shocks (repositioning campaigns, cultural shifts) confront an asymmetric recovery problem: some regain cohort separability while others enter absorbing cross-cohort interference. Modeling cohort perception clouds as almost-invariant sets in a stochastic flow on the eight-dimensional SBT perception manifold — with separability governed by the spectral gap of the perception operator — yields a closed-form sufficient condition for separability survival: the corrective coherence emission rate μ must exceed the spectral leakage rate λ at the observer cohort's detection scale δ (μ > λ at scale δ). The threshold follows from Kato–Rellich perturbation theory and Diaconis–Stroock spectral-gap bounds for reversible Markov chains. A Monte Carlo demonstration seeded with author-proposed Dove-calibrated parameters (λ ≈.10/year, μ ≈ 4.50/year) shows the inequality correctly separates a recoverable regime (terminal mean gap 1.10) from an absorbing regime (terminal mean gap.02), and that spectral-gap collapse precedes conviction reorientation by 6–18 months — a leading indicator unavailable from traditional perceptual maps or aggregate VECMs.", "n_prop_claims": 11, "terms": { "owns": [ "cohort-separability", "corrective-coherence-emission-rate", "spectral-gap-restoration-threshold", "spectral-leakage-rate" ], "imports": [ "absorbing-state", "cohort", "non-ergodic-perception", "perception-cloud", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026ae", "title": "Verification as Operator: Spectral Projection, Rank Deficiencies, and the Persistence of the Audit Society", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19778588", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/verification-as-operator", "thesis": "Organizational verification is formally a spectral projection operator P that maps organizational states onto invariant subspaces defined by acceptance criteria, satisfying idempotency (P^2 = P) and self-adjointness (P* = P). A state passes verification iff it already lies in that invariant subspace (P(s) = s). Conventional compliance audit is a degenerate rank-1 projection onto a single compliance axis and therefore discards, by construction, all organizational performance information orthogonal to that axis — the algebraic root of the information loss the audit-society literature documents. The acceptance-testing cascade of Organizational Schema Theory is, by contrast, a full-rank projection in which each hierarchical level independently projects onto a distinct performance subspace, preserving the dimensional structure of the specification. Cybernetics, behavioral organization theory, and software engineering verification each implicitly instantiate the same projection identity without naming it. Three propositions establish the rank inequality between audit and cascade, the cascade-consistency condition required for full-rank operation, and the bandwidth bound on sustainable projection rank; a six-dimensional simulation shows rank-1 audit leaves approximately 90% of organizational deviation undetected. The audit society is thus the equilibrium under a rank-1 bandwidth budget, not a pathology — and verification rank, not audit rigor, is the lever for substantive alignment.", "n_prop_claims": 10, "terms": { "owns": [ "cascade-consistency-condition", "full-rank-cascade", "rank-1-audit", "spectral-projection-operator", "verification-as-operator", "verification-bandwidth" ], "imports": [ "re-collapse", "six-tier-ontology", "spectral-dimensions" ], "refines": [] } }, { "key": "2026af", "title": "Organizational Metamerism: Observer-Relative State Equivalence in Organizational Configurations", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19869871", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/org-as-metadata", "thesis": "Structurally distinct organizations can produce value outputs that a given evaluative observer cannot tell apart while executing the same process. This paper names that condition organizational metamerism — an observer-relative, process-relative STATE equivalence (distinct configurations equivalent NOW), not the PATH equivalence that equifinality describes (different histories reaching the same end state). Metamerism is borrowed from color science, where two distinct spectral distributions match for a particular observer under a particular illuminant, and is lifted one level up from the brand-signal metamerism of the corpus's spectral brand theory to whole organizational configurations. The phenomenon rests on a temporal stability hierarchy — value outputs change more slowly than processes, which change more slowly than configurations — explained by an organization-as-metadata mechanism: form is the revisable configuration layer for processes, not the productive logic itself, so it can be re-specified (a schema migration) without altering what is produced, provided the migration is lossless. The size of the metamerism set M(P,O) is a derived quantity: it expands as coordination logic is absorbed into process specifications (falling coordination cost) and contracts as the tacit knowledge intensity of the process rises. The framework yields four testable propositions with explicit confirmation/falsification criteria, most notably that AI-mediated coordination decouples organizational-restructuring frequency from process-change frequency, bounded by tacit knowledge intensity.", "n_prop_claims": 10, "terms": { "owns": [ "metamerism-set", "organization-as-metadata", "organizational-layer", "organizational-metamerism", "temporal-stability-hierarchy", "value-layer" ], "imports": [ "cohort", "observer-spectral-profile", "six-tier-ontology", "spectral-dimensions" ], "refines": [] } }, { "key": "2026ag", "title": "Dual Hierarchies of Organizational Transferability: A Six-Tier Ontology and Theory of Acquisition Failure Propagation", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19895813", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/six-tier-ontology", "thesis": "Mergers and acquisitions destroy value at high rates because the field lacks a shared ontology specifying which organizational layers transfer and how failures propagate across them. This paper develops a six-tier ontology of the acquisition target — Owner Intent, Business Model, Business Entity, Product, Process, Organization — each with a distinct governor, specification surface, and transferability mode. The tiers form two oppositely directed hierarchies: a service hierarchy upward (Organization to Intent) and a constraint hierarchy downward (Intent to Organization). The constraint hierarchy fixes integration sequencing; shocks propagate bidirectionally, yielding seven falsifiable failure-propagation propositions. The framework is form-invariant across for-profit, NGO, and cooperative entities via explicit substitution rules (Tiers 2, 4, 5 provisional), and derives a Six-Tier Separability Diagnostic (STSD) as a theoretical implication. The primary contribution is a generalizable theory of organizational separability under ownership change: separability is never costless because constraint architectures are sticky.", "n_prop_claims": 21, "terms": { "owns": [ "six-tier-ontology", "tier-1-owner-intent", "tier-2-business-model", "tier-3-business-entity", "tier-4-product", "tier-5-process", "tier-6-organization" ], "imports": [], "refines": [] } }, { "key": "2026ah", "title": "Brand as a Modular Layer: Tiered Organizational Architecture, Separability, and Firm Performance in Multi-Brand Strategies", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19930157", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/brand-as-modular-layer", "thesis": "Firms differ dramatically in their ability to host multiple brands, recover from brand failure, and organize marketing — yet no theory specifies which organizational layer carries the brand boundary. This paper proposes that brand IS strictly the Tier-4 product specification surface in the six-tier architecture of Zharnikov (2026ag); Tiers 1 (Owner Intent), 2 (Business Model), 3 (Business Entity), 5 (Process), and 6 (Organization) are predominantly brand-agnostic. Three strategic outcomes follow from this single structural fact. Multi-brand capacity scales with Tier-3/5/6 separability rather than Business-Model diversification (P1); failed-brand recovery success scales with preserved brand-agnostic substrate (P2), supplying a mechanism for the equity-transfer-without-creation regularity of Marques et al. (2020); marketing, advertising, and branding are Tier-6 functions that create, operate, and retire Tier-4 instances, so centralization choices are separability choices (P4). The Aaker-Joachimsthaler Brand Relationship Spectrum is operationalized as a continuous Tier-3-visibility-in-Tier-4 parameter V (P7), and axis-specific brand-extension predictions follow on the Cultural and Ideological SBT dimensions (P5). Two diagnostic instruments (Multi-Brand Capacity Diagnostic, Recovery Salvage Matrix) translate the framework for practice. Seven falsifiable propositions unify the brand-portfolio, corporate-rebranding, and marketing-organization literatures under one modularity logic. This is a theory-building contribution; empirical validation is a four-priority roadmap.", "n_prop_claims": 11, "terms": { "owns": [ "brand-agnostic-brand-bound-decomposition", "brand-as-tier-4-projection", "multi-brand-capacity-diagnostic", "recovery-salvage-matrix", "tier-3-visibility-in-tier-4" ], "imports": [ "brand-conviction", "cohort", "observer-spectral-profile", "perception-cloud", "re-collapse", "six-tier-ontology", "spectral-brand-theory", "spectral-dimensions", "tier-1-owner-intent", "tier-2-business-model", "tier-3-business-entity", "tier-4-product", "tier-5-process", "tier-6-organization" ], "refines": [] } }, { "key": "2026ai", "title": "The Tier-Rotation Curve: A Theory of Brand-Substrate Decoupling and Its M&A-Value Geometry", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20069605", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/tier-rotation", "thesis": "Deal outcomes for founder-led branded firms diverge sharply even among principals of comparable quality and brand strength, and that divergence is explained by the proportion of brand conviction that has been externalized from the founder's personal judgment (Tier 1) into an organizational substrate the acquirer can own independently (Tier 4). Brand signal accumulates in the Tier-4 substrate along a logistic trajectory governed by sustained knowledge-externalization effort, a cold-start offset, and sector substitutability; acquirer willingness-to-pay is a piecewise function of Tier-4 share with a separability kink, below which founder-flight risk produces discounts and earnouts and above which the brand commands a premium increasing with sector substitutability. The resulting non-monotonic value geometry — value rising everywhere but with a discontinuous slope at the kink — yields within-founder longitudinal predictions unavailable to cross-sectional human-capital or succession-discount theories, grounds the accumulation in Nonaka and Takeuchi's SECI externalization mechanism with four observable proxies, and endogenizes the resource-based view's exogenous resource-mobility assumption for brand assets. The contribution is theoretical: a mechanism-based geometry supplying five falsifiable propositions, not new empirical analysis.", "n_prop_claims": 12, "terms": { "owns": [ "rotation-effort-intensity", "separability-kink", "tier-4-share", "tier-rotation", "tier-rotation-curve" ], "imports": [ "absorbing-state", "brand-conviction", "observer-spectral-profile", "perception-cloud", "six-tier-ontology", "tier-1-owner-intent", "tier-4-product" ], "refines": [] } }, { "key": "2026aj", "title": "Where to Invest Within the Firm: Organizational Tiers, Discount Rates, and AI Penetration", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20072288", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/tier-allocation", "thesis": "Investment direction within a firm — not merely investment intensity — is the consequential strategic choice. Two firms with identical revenues, margins, and aggregate investment can generate exit multiples of 2x versus 9x because they routed investment to organizational tiers that differ in substrate durability. The paper formalizes cross-tier allocation as a discounted Cobb-Douglas aggregator over a six-tier hierarchy with tier-specific decay rates delta_t (.50/year at the organizational surface down to.05-.10/year at foundational layers) and Jorgensonian per-tier user costs (delta_t + r). Optimizing subject to the rental-rate budget constraint yields the closed-form rule w_t*(r) = alpha_t / (delta_t + r) and the comparative static d w_6*/dr > 0: higher-discount-rate principals optimally over-allocate to the high-decay surface tier. Four propositions link pre-deal surface-tier intensity, governance horizon, cost-of-capital shocks, and capability-rotation stage to M&A outcomes. Part II perturbs the same primitives with two AI-specific shocks per tier — a cost shock gamma_t and a durability shock Delta_t — yielding the generalized rule w_t*(r; gamma, Delta) = alpha_t / [gamma_t * (delta_t^eff + r)] and three further propositions: surface-tier (Tier 6) AI raises short-run earnings yet lowers long-run multiples; a discrete substrate-building threshold exists at Tier 4; and AI's net value effect flips sign with the principal's effective discount rate. The tier — not the division, the capability, or the resource — is the missing architectural unit of allocation.", "n_prop_claims": 10, "terms": { "owns": [ "tier-allocation", "tier-independence-overestimation", "tier-specific-decay-rate" ], "imports": [ "six-tier-ontology", "tier-1-owner-intent", "tier-2-business-model", "tier-3-business-entity", "tier-4-product", "tier-5-process", "tier-6-organization", "tier-rotation", "tier-rotation-curve" ], "refines": [] } }, { "key": "2026al", "title": "Capability as Projection of an Append-Only Organizational Log: An Event-Sourced Substrate Theory of Organizational Capability and Transfer Failure", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20367459", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/capability-as-projection", "thesis": "Organizational capability is not a stored stock of resources or routines but a render-time projection of an append-only log of immutable events — the decisions, failures, policies, hires, and artifacts through which the capability was actually produced. The paper specifies three formal objects (a partially ordered event log L, a projection operator pi that reads the log under a query at a render time, and a compatibility function kappa scoring log-merge events such as acquisitions) and derives four propositions about capability transfer: clean log merges preserve projection continuity; snapshot imports without the underlying log diverge within three years; writedown magnitude in failed M&A is jointly determined by raw log incompatibility AND the acquirer's integration-policy choice; and imitators who observe only the projection cannot replicate capability responses to novel queries. The substrate-projection distinction reframes the long-running tautology critique of dynamic capabilities as a category error and generates falsifiable predictions about transfer failure. The contribution is substrate-layer, not a wholesale recasting of the firm.", "n_prop_claims": 14, "terms": { "owns": [ "append-only-organizational-log", "capability-as-projection", "log-compatibility-function", "projection-operator", "snapshot-versus-rendering" ], "imports": [ "six-tier-ontology" ], "refines": [] } }, { "key": "2026am", "title": "Specification Readiness and Endogenous Friction: An Information-Theoretic Model of Multi-Interface Organizational Architecture", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20379981", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/specification-readiness", "thesis": "Alignment friction between an organization and its heterogeneous audiences is endogenous to specification codification, not an exogenous feature of the environment. Organizational output architecture decomposes into three layers: a codified specification substrate encoding commitments across six ontological tiers; an interface layer in which the substrate is rendered to N (canonically six) recipient classes, each characterized by a distinct perception-weight vector w_i; and a function layer whose headcount and spend constitute a measurable tax on specification gaps. Under push regimes, energy loss scales with the cross-entropy between the firm's guessed and the recipient's actual need profile; under pull regimes, consumption-layer AI lets recipients query the substrate directly, collapsing misalignment toward zero as codification completeness rises. Four contributions follow: push-pull cost asymmetry formalized as a structural analog to Shannon cross-entropy; geometric machinery (perception-weight vectors + a cross-class coherence condition) linking substrate to interface rendering; functional friction derived as a consequence of specification investment rather than governance choice; and specification readiness identified as the critical moderator of AI returns, distinguishing Substrate-Operator from Surface-Operator execution. Specification codification is architecturally prior to governance and capability deployment, generating predictions distinct from transaction-cost economics, stakeholder theory, and AI-augmentation scholarship.", "n_prop_claims": 10, "terms": { "owns": [ "function-as-friction-tax", "multi-interface-specification-model", "recipient-class", "specification-readiness", "substrate-operator" ], "imports": [ "six-tier-ontology", "tier-1-owner-intent", "tier-2-business-model", "tier-3-business-entity", "tier-4-product", "tier-5-process", "tier-6-organization" ], "refines": [] } }, { "key": "2026an", "title": "Specification Readiness: Measuring an Architectural Antecedent of Functional Friction and AI Returns", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20384084", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/specification-readiness-empirical", "thesis": "Specification readiness — the degree to which a firm's commitments are codified in versioned, machine-readable, queryable form — is a measurable firm-year strategic construct that is conceptually prior to organization capital, brand capital, and disclosure readability. A continuous Specification Coherence Index (SCI), built from within-firm year-over-year cosine similarity of 10-K narrative embeddings, supplies the first scalable archival operationalization across the Compustat universe of US public firms 2010–2025; a four-event sharp index supplies discrete robustness. The construct is argued to substitute query-based alignment for costly interface-maintenance functions, reducing a structural friction tax (H1), redirecting marketing spend toward brand-capital accumulation (H2), lowering cross-stakeholder valuation dispersion under incoherence (H3), raising returns to AI deployment (H4), and governing the valuation consequence of advertising-spend cessation (H5). A multi-arm identification template pairs continuous within-firm treatment with staggered difference-in-differences (Callaway-Sant'Anna; Goodman-Bacon), regulatory-compliance instruments, and advertising-cessation event studies, disciplined by an Oster (2019) threats register. Pre-registered Monte Carlo mechanism tests (12.96 million trials; α* =.91; Cohen's d = 88.4) confirm the friction-tax phase shift, and a regression-identification simulation confirms power ≥.80 for all five hypotheses at the pre-registered effect sizes. The paper contributes the measure, the reusable identification template, and formal evidence that specification readiness moderates the AI augmentation paradox; the archival panel estimates implementing the design are in execution as a companion.", "n_prop_claims": 10, "terms": { "owns": [ "specification-coherence-index" ], "imports": [ "multi-interface-specification-model", "six-tier-ontology", "specification-readiness", "tier-1-owner-intent", "tier-2-business-model", "tier-3-business-entity", "tier-4-product", "tier-5-process", "tier-6-organization" ], "refines": [] } }, { "key": "2026ao", "title": "Spec-Based Research in the Post-AI Era: A Cost-Asymmetry Theory of Meaning and Meaningfulness in Organizational Knowledge Work", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20409683", "github_url": "https://github.com/spectralbranding/meaningfulness-papers/tree/main/meaning-meaningfulness", "thesis": "Generative AI shifts the cost-structure of knowledge work asymmetrically across the three-level hierarchy of scholarly artifacts (log → semantic graph → rendering). Meaning (the graph-extractable structure of claims, dependencies, and evidence) becomes cheap to verify and recombine at scale; meaningfulness (the context-dependent prose realization for a specific cohort) does not, and may become more costly relative to the new equilibrium. This asymmetry creates a management-theoretic cost-allocation problem. The three-level hierarchy is the analytical tool; the spine-first drafting protocol is the prescriptive intervention; the SPINE.yaml v0.2 schema is the operational artifact — and its intentional complexity is the first operationalization of the cost-asymmetry result: a schema that is unwieldy for a human to author top-to-bottom is exactly what the cost-asymmetry predicts, because the spine is the meaning-operations layer where AI's comparative advantage is largest. The paper exhibits the post-AI knowledge-work organizational form by building it. The primary contribution is the Operator role and its era-dependent projection of structural-versus-judgment operations; the cost-asymmetry mechanism, the typed-DAG specification, the three-level hierarchy, the SPINE.yaml v0.2 schema, and the spine-first drafting protocol are operationalizations of that role-theoretic move. Two propositions are primary — P1 (separability) and P4 (rendering-equivalence under spine-preservation); P2 (recombination) and P3 (verification-cost asymmetry) are stated as theoretically-derived predictions with explicit falsifiers, with full empirical estimation the scope of the empirical companion. Five validation cases illustrate P1 and P4 at the depth a theoretical contribution requires: a contemporary management-theory twin pair as the primary illustrative case; a multi- author position essay on AI in research as a venue-fit contemporary anchor; the founding papers of quantum mechanics as a historical existence proof; a forward-looking application to an external organizational artifact; and the reflexive self-application of the framework to this paper's own production.", "n_prop_claims": 5, "terms": { "owns": [ "meaning-vs-meaningfulness", "operator-role", "rendering-equivalence", "spine", "spine-first-drafting-protocol" ], "imports": [], "refines": [] } }, { "key": "2026ap", "title": "Same Meaning, Different Prose: Spine Preservation and Rendering Equivalence in Organizational Knowledge Work", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20409701", "github_url": "https://github.com/spectralbranding/meaningfulness-papers/tree/main/meaning-meaningfulness-empirical", "thesis": "Paper A 2026ao states P4 (rendering-equivalence under spine-preservation) as a primary preservation theorem: two prose renderings of a locked substrate converge on conclusions if and only if both renderings preserve the spine's structural elements, under axiom A1 (σ-faithfulness on locked subsets). Paper B is the empirical companion. Its central contribution is an empirical demonstration of paper_a:P4 on management- theory twin pairs: two independently-extracted source papers produced as separate prose renderings share a substrate at Rec = 4 linked propositions with preserved antecedents on BOTH available pairs (focal: Eisenhardt-Martin 2000 + Zollo-Winter 2002; KBV: Grant 1996 + Liebeskind 1996). Each twin pair is treated as one example of two prose renderings that share an underlying substrate — not as a Bikard test of recombination-rate (P2) nor as a calibration of cost-asymmetry-driven recombination thresholds (P3). Secondary contributions are: grid-anchored illustrative estimates of β and δ across five available spines and renderings, reported as supportive of the paper_a:P3 ordering β < 1 < δ; and a pre-registered iterative-cohort-growth protocol with Zenodo-DOI-per- version discipline that turns the working-paper trajectory itself into a longitudinal self-test of paper_a:P4 (each Paper B release is a rendering of a growing substrate). The task set adds self-application to Paper B's own spine, third-rendering of the focal-pair shared substrate, cross-language re-rendering, and inter-coder κ measurement on axiom A1.", "n_prop_claims": 25, "terms": { "owns": [], "imports": [ "meaning-vs-meaningfulness", "rendering-equivalence", "spine", "spine-first-drafting-protocol" ], "refines": [] } }, { "key": "2026aq", "title": "Value Headroom Moderates Whether Specification Beats Style in LLM Negotiation", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20595996", "github_url": "https://github.com/spectralbranding/negotiation-spec-experiment/tree/main", "thesis": "Value headroom — how much joint surplus a naively cooperative pair leaves on the table — is a first-order moderator of prompt-type efficacy in dyadic LLM negotiation. Interpersonal style (warmth) dominates structural specification only when joint-value headroom approaches zero; above a modest headroom threshold, specification-first prompting produces strictly higher expected value while remaining affectively neutral. The specification advantage (1) is mechanistically due to a taught integrative procedure — logrolling — not to leakage of the payoff matrix; (2) is robust to prompt paraphrase; (3) grows with model capability; and (4) replicates across model families. This reframes an apparent \"style beats structure\" result reported on near-ceiling scenarios as a boundary case of a more general headroom-dependent law.", "n_prop_claims": 6, "terms": { "owns": [ "value-headroom" ], "imports": [], "refines": [] } }, { "key": "2026ar", "title": "The OrgSchema Audit: A Six-Level Diagnostic for Specification-Driven Organizations", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19555201", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/orgschema-audit", "thesis": "A significant share of organizational dysfunction originates not from poor execution but from absent or misaligned specifications. The OrgSchema Audit operationalizes Organizational Schema Theory's six-level specification cascade (experience contracts, signal requirements, process contracts, procedures, input specifications, sourcing requirements) into a replicable, practitioner- executable diagnostic protocol with explicit healthy/failing criteria and fixes at each level. The protocol parallels the Spectral Audit for brand perception but targets organizational operations rather than perceptual allocation. It advances two testable propositions — that specification failures at higher cascade levels predict greater dysfunction than lower-level failures (cascade-position prioritization), and that complete bidirectional traceability yields measurable operational benefits over partial traceability — and demonstrates the full protocol on a worked example (Spectra Coffee). Remediation should be prioritized by cascade position rather than symptom severity. The audit is executable with or without AI, though large language models substantially reduce the cost of initial specification extraction.", "n_prop_claims": 11, "terms": { "owns": [ "cascade-position-prioritization", "orgschema-audit", "specification-maturity" ], "imports": [ "brand-conviction", "cohort", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026as", "title": "PRISM: A Structured Measurement Instrument for Multi-Dimensional Brand Perception", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19555265", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/prism-instrument", "thesis": "Measuring brand perception requires an instrument that captures multi-dimensional structure rather than collapsing it to a single equity score, and that can be administered to AI and human observers on a common scale. Existing multi-dimensional instruments (Aaker BPS, Brakus BXS, Yoo-Donthu CBBE, Geuens et al.) derive their dimensions empirically from human response factors and so are human-specific; an instrument for commensurable AI-human measurement must instead derive dimensions from the signal side, which Spectral Brand Theory supplies. This paper specifies PRISM (Perception Response Instrument for Structured Measurement): a domain-neutral five-layer scaffold (PL0 specification, PL1 configuration, PL2 prompts, PL3 sessions, PL4 analysis), the complete PRISM-B brand variant (eight items mapped one-to-one to the eight SBT dimensions, a 1--5 ordinal response format shown to be the minimum-distortion operating point for AI observers, an exact prompt template, and a scoring algorithm comprising the Dimensional Collapse Index and cross-observer cosine convergence), and the instrument's connection to multi-observer triangulation via Perception DOP. Specification is deliberately separated from validation: the instrument is fixed here so that a later human-subject study has a stable target.", "n_prop_claims": 15, "terms": { "owns": [ "prism-b", "prism-five-layer-scaffold", "prism-instrument" ], "imports": [ "brand-conviction", "cohort", "dimensional-collapse-index", "observer-spectral-profile", "perception-cloud", "perception-dop", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026at", "title": "Negotiating Vocabularies at Link Time: A Deterministic Six-Class Compatibility Check for Federated Ontology Modules", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20751395", "github_url": "https://github.com/spectralbranding/federated-negotiation/tree/main", "thesis": "The link-time compatibility check that compilers and package managers apply to code — refuse to build when two components make incompatible demands on a shared symbol, and name exactly which two disagree — transfers to scholarly vocabularies. If each work declares the terms it owns, imports, and refines as a small content-addressed module, a federated linker classifies every cross-author interaction into exactly one of six classes (AGREEMENT, CROSS_IMPORT, CROSS_REFINE, CONFLICT, INCOMPATIBLE_REFINE, DANGLING_IMPORT), proposes a typed and justified SSSOM reconciliation, and fails a continuous-integration gate on the three unresolved classes — before either author reads the other's prose. The classification is a deterministic pure function of two parsed module sets grounded in content-addressed definition-hash identity; it occupies the zero-uncertainty, syntactic/element-level corner of the ontology-matching space and adds the interaction-classification + reconciliation-operation + CI-gate layer that the matching literature leaves to post-hoc human judgment. The paper formalizes the taxonomy, implements it as a dependency-light reference tool, and evaluates it on three real, independent vocabulary pairs that together exercise the full interaction-class set.", "n_prop_claims": 6, "terms": { "owns": [ "agreement-class", "conflict-class", "content-addressed-module", "cross-import-class", "cross-refine-class", "dangling-import-class", "def-hash-identity", "federated-ci-gate", "federated-ontology-negotiation", "incompatible-refine-class", "interaction-class", "reconciliation-operation" ], "imports": [ "cohort", "peer-alignment-event", "perception-cloud", "research-as-repository", "spectral-dimensions", "substrate-as-repository" ], "refines": [ "link-time-compatibility-check" ] } }, { "key": "2026au", "title": "The Correspondence Principle of Brand Management", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20757596", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/brand-correspondence-principle", "thesis": "The incumbent brand-equity frameworks — Aaker's brand equity, Keller's customer-based brand equity, Kapferer's identity prism, the Ehrenberg-Bass distinctiveness school, and single-figure brand valuation — are not rivals to Spectral Brand Theory (SBT) but its limiting cases. Modeling a brand as an observer-completed probability measure mu on an eight-dimensional perception manifold, each incumbent is represented as a measurable projection-and-aggregation operator T_k that induces a Blackwell garbling of the full perception measurement (the representation lemma). Two theorems follow. The CORRESPONDENCE THEOREM: the aggregate brand-health score is a sufficient statistic for the managerial decision problem if and only if four regime conditions hold jointly (a tight unimodal cloud; slow temporal dynamics; a human-only observer set; a firm-dominated signal); in that corner SBT reduces to the incumbent, which is why the incumbent worked, and the Ehrenberg-Bass \"brands differ little in image\" finding is relocated as an empirical diagnosis of which regime a category occupies, not a universal law. The DECISION-EFFICIENCY THEOREMS: outside that corner the score is a garbling of the cloud, so the full measurement weakly dominates the score for every decision-maker (directed-gradient dominance), and the realized decision loss is bounded below by a quantity monotone in four regime-departure parameters (metameric arbitrage). The theorems entail a manager-runnable decision procedure — regime test, blind-spot diagnostic, directed-intervention rule, metameric-substitution rule — realized in an atomic-perception measurement architecture. SBT is brand metrology (the astronomer), not brand management (the astronaut); Blackwell's theorem is the bridge by which finer measurement provably helps every mission without SBT being a theory of any mission.", "n_prop_claims": 7, "terms": { "owns": [ "blind-spend", "brand-management-correspondence-theorem", "brand-metrology", "classical-brand-regime", "directed-gradient-dominance", "incumbent-garbling-operator", "metameric-arbitrage", "regime-departure-parameter", "regime-test" ], "imports": [ "brand-conviction", "cohort", "dimensional-collapse", "metameric-observer", "non-ergodic-perception", "observer-spectral-profile", "perception-cloud", "re-collapse", "spectral-brand-theory", "spectral-dimensions", "spectral-metamerism" ], "refines": [] } }, { "key": "2026av", "title": "Reaching a Perception: From Perceptual Cohort to Reachable Audience", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20765556", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/reaching-a-perception", "thesis": "The correspondence principle (2026au) shows that an aggregate brand score is a Blackwell garbling of the eight-dimensional perception cloud and prescribes acting on the highest- payoff (dimension, cohort) — the directed-intervention rule P6. But P6 presumes a cohort is ACTIONABLE without showing it is REACHABLE: a cohort defined by perceptual proximity has no native media address, unlike the addressable audiences (channels, cookies, lookalikes) of traditional activation. This applied companion closes that gap. \"Actionable\" decomposes into three measurable bridge mechanisms from perception space to action, unified by a measurement->activation HANDOFF CONTRACT consistent with SBT's metrology posture (the astronomer supplies coordinates and the bridge cost; the manager flies): (b) BROADCAST-A-DIMENSION — emit on the dimension the cohort is sensitive to and let self-selection route the signal; zero address required. Formally a separating signal on a degraded broadcast channel (Cover 1972): the observer's channel quality is the inner product of the signal vector with the observer's spectral-sensitivity vector, so off-peak observers receive a metamer-to-null. The self-selection sharpness equals the same sin^2(beta) that the parent paper counts as a perception-metamerism LOSS: the targeting BUG becomes a self-selection FILTER. This is the headline. (c) PROVENANCE-AS-ADDRESS — the reflection-based perception architecture's reflections carry the surfaces (and recency) where each perception was found; a cohort of reflections traces back to re-reachable channels. (a) PERCEPTION->PROXY JOIN — map the cohort to addressable proxies and QUANTIFY the Blackwell-garbling decision loss L(P) of doing so; report the minimal-loss proxy P*. The reach answer is a structural TAILWIND, not a patch: the only route needing an address (a) is a measurable, lossy projection, and the address-free route (b) is exactly where post- cookie activation is already heading (the industry's own Topics-API cohort pivot), so SBT does not depend on the identity-addressability the advertising industry is losing. The individual observer spectral profile is the primitive; cohorts are derived clusters in that space.", "n_prop_claims": 4, "terms": { "owns": [ "broadcast-a-dimension", "measurement-to-activation-handoff-contract", "perception-to-proxy-join", "provenance-as-address", "proxy-join-loss", "resonance-bandwidth", "self-selection-filter" ], "imports": [ "brand-metrology", "cohort", "dimensional-collapse", "incumbent-garbling-operator", "metameric-arbitrage", "metameric-observer", "observer-spectral-profile", "perception-cloud", "spectral-brand-theory", "spectral-dimensions", "spectral-metamerism" ], "refines": [ "metameric-arbitrage" ] } }, { "key": "2026aw", "title": "Forming a Perception: Campaigns as Forcing Functions and the Relaxation of the Brand Perception Cloud", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20769594", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/forming-a-perception", "thesis": "A marketing campaign is an exogenous force on a multi-dimensional perceptual state, and the observable practitioners call \"perception decay when advertising stops\" is the unforced relaxation of that state back toward a brand-specific stable point. This paper formalizes perception formation and maintenance as a FORCED DYNAMICAL SYSTEM whose results stand on the stochastic-dynamics math alone, independent of any one perceptual instrument. The perception cloud is a probability measure mu_t on a fixed K-dimensional perceptual space (here K=8, but the results hold for any fixed perceptual basis); its centroid x_bar(t) = E[X_t] obeys a forced Ornstein-Uhlenbeck SDE dX = [ -A (X - x*) + F(t) ] dt + Sigma dW, where x* is the brand's intrinsic stable point (the perception it relaxes toward unforced), A is the positive-definite restoring/relaxation operator, F(t) is the campaign's FORCING FUNCTION (a vector in the same perceptual basis as the cloud), and Sigma dW is generic perceptual diffusion. FORMATION is the forced transient toward a target; MAINTENANCE is sustained forcing balancing relaxation; the \"stop advertising -> perception decays\" folklore is the unforced (F=0) relaxation of the centroid toward x*, with a measurable PERCEPTION-DECAY TIME CONSTANT tau = 1 / lambda_min(A) (inverse of the slowest relaxation rate). The instrument recovers F and tau from a TIME-SLICED perceptual series (any dated perceptual-tracking series) spanning a spend pulse. The unifying result ties formation to reach: a brand's off-generic DISTINCTIVENESS — the off-generic energy share of its centered profile — LOWER-BOUNDS the persistence time tau of its formed perception, because a more distinctive brand sits FARTHER OUTSIDE the dense, localized generic attractor, where that attractor adds LESS restoring curvature to its well, so lambda_min is smaller and the perception relaxes more slowly. This ordering, ASSERTED through the toy law lambda(s)=lambda_0(1-kappa*s), is DERIVED in the Electronic Companion (EC.3) from a single stated, defended curvature primitive (P-CURV: a dense localized attractor contributes restoring curvature that falls with separation), and the toy law is recovered as its local linearization. The forced-OU vector model NESTS the scalar prior art: project onto one dimension and add an information reading of F and the Erdem-Keane Bayesian scalar-quality-learning updating is recovered as the 1-D special case, just as Nerlove-Arrow goodwill and Vidale-Wolfe response are its 1-D shadow. Spectral Brand Theory is named ONCE as the empirical instantiation (the K=8 perceptual basis); the paper is otherwise corpus-independent — a reader with zero corpus access verifies every proposition. Metrology posture holds: the instrument measures cloud position, the campaign's forcing, and the forcing-vs-relaxation budget; the manager runs the campaign. NARROWED lead claim: we FORMALIZE perception formation as forced relaxation on a perceptual manifold and DEMONSTRATE (calibrated simulation — an existence proof of the ordering mechanism, NOT a field test) that distinctiveness lower-bounds persistence; the confirmatory panel design is a roadmap.", "n_prop_claims": 5, "terms": { "owns": [ "distinctiveness-persistence-ordering", "forced-perception-dynamics", "forcing-function", "maintenance-forcing-budget", "perception-decay-time-constant", "perceptual-stable-point" ], "imports": [ "brand-metrology", "cohort", "observer-spectral-profile", "perception-cloud", "re-collapse", "self-selection-filter", "spectral-brand-theory", "spectral-dimensions", "spectral-dynamics", "spectral-metamerism" ], "refines": [ "spectral-dynamics" ] } }, { "key": "2026ax", "title": "The Brand Spectrometer: A Reproducible Instrument for Cohort-Resolved, Multi-Dimensional Brand-Perception Measurement from Public Artifacts", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20775963", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/brand-spectrometer-methods", "thesis": "The Brand Spectrometer is a measurement instrument, not a brand oracle. It reconstructs cohort-resolved eight-dimensional brand-perception spec vectors from public artifacts through a fixed open pipeline (acquire -> render -> extract -> aggregate -> sensitivity) operated by cross-family LLM pairs. Because brand perception is ground-truth-absent — cohort metameric variance IS the measurement, not error around a latent true spec — the instrument is validated for its MEASUREMENT PROPERTIES against two noise floors it computes for itself (an operator floor from cross-family alt-pairs; an artifact floor from leave-one-out), never for criterion accuracy. A pre-registered V1-V5 battery across two adjacent sampling windows of one topical case shows the instrument is reliable (test-retest within the operator floor), cross-operator reliable, convergent-valid, reproducible (byte-identical re-derivation, no keys), and structurally valid: it resolves cohort differences exceeding its floors and DECLINES to manufacture differences it cannot separate from operator noise. Discriminant resolution is METRIC-dependent: a scale-invariant mean-cosine signal-to-noise abstains on both windows, while a distribution-level, operator-floored criterion resolves the owner cohort from the press in the fresh window (a magnitude separation triangulated across an energy-distance permutation test, a kernel MMD, and a bootstrap interval, and reported as EXPLORATORY because the metric was chosen after the confirmatory null). We name this validation class metameric psychometrics: reliability, cross-operator reliability, convergent validity, and reproducibility hold unconditionally; discriminant resolution is conditional on cohort signal exceeding the instrument's own noise in the structure a given metric can see (shape vs magnitude-and-distribution).", "n_prop_claims": 9, "terms": { "owns": [ "artifact-noise-floor", "atlas", "brand-spectrometer", "distributional-separation-metric", "metameric-degree", "metameric-psychometrics", "operator-noise-floor", "per-pair-resolution-criterion", "reflection", "signal-source-clustering", "triangulation-resolution-criterion", "two-window-falsification" ], "imports": [ "atom", "brand-metrology", "cohort", "observer-spectral-profile", "perception-cloud", "prism-c", "prism-m", "prism-t", "spectral-brand-theory", "spectral-dimensions", "spectral-metamerism", "version-epoch", "version-floor" ], "refines": [ "brand-metrology" ] } }, { "key": "2026ay", "title": "The Substrate Floor: Nested Noise Floors for Auditable Abstention Across Heterogeneous Instruments", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20840422", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/substrate-floor", "thesis": "Honest abstention generalizes from one measurement instrument to an ensemble of heterogeneous instruments under a single rule: a finding survives only if its signal clears the OUTERMOST noise floor in play, where floors NEST — operator ⊆ artifact ⊆ substrate. The same discipline that lets one measurement instrument abstain below its operator/artifact noise floor lets a CROSS-INSTRUMENT ensemble abstain below a SUBSTRATE FLOOR (the dispersion of instruments' verdicts on one aligned claim) and lets a SPECIFICATION-based instrument abstain below a COHERENCE FLOOR (incoherence 1−SCI plus an audit-coverage gap). Reconciliation returns a TYPED VERDICT — corroborated / contested / substrate-conditional / jointly-unresolved — never a forced point estimate: cross-instrument agreement is triangulation, disagreement is the floor itself. The mechanism is live meta-analysis across instruments — report the heterogeneity, do not pool it away — but it goes past heterogeneity reporting in three ways that standard methods cannot reproduce (P4): (i) it composes instruments of different KINDS that share no output space, reconciling an 8-dimensional measurement vector and a categorical specification audit on the aligned claim's verdict rather than their incommensurable raw outputs; (ii) a no-rescue lemma forbids agreement among individually-noisy instruments from manufacturing a finding; (iii) below the coherence floor abstention is MANDATED by a geometric coverage-impossibility result, not chosen by convention. The contribution is the open-source computational framework (already shipped) that operationalizes this — not a relabeling of heterogeneity statistics, sensor fusion, metrology uncertainty budgets, or selective prediction, but a typed-verdict lattice over nested floors that returns verdicts those four literatures, by construction, do not.", "n_prop_claims": 5, "terms": { "owns": [ "coherence-floor", "cross-substrate-dispersion", "floor-nesting", "reconciliation-lattice", "substrate-floor" ], "imports": [ "cohort", "federated-ontology-negotiation", "orgschema-audit", "specification-coherence-index", "spectral-metamerism" ], "refines": [] } }, { "key": "2026az", "title": "Measuring Perceptual Indistinguishability: A Pre-Registered Metamerism Instrument for AI Brand Perception (PRISM-M)", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.21125785", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/prism-m-metamerism", "thesis": "Indistinguishability under a coarse readout is measurable, not assertable. PRISM-M supplies a general dual-floor procedure for testing observational equivalence in any high-dimensional perceptual instrument — a pair of entities counts as a measured metamer only when the full readout resolves them beyond the instrument's own operator noise floor while the coarse readout (its own floor measured separately) does not — and demonstrates the procedure end-to-end on AI brand perception, where the eight-dimension profile is the full readout and a brand-health score, a recommendation ranking, and a binary pick are the aggregators under test. The pre-registered campaign returns a boundary result that showcases the discipline: with four cross-family operator pairs, one renderer reads brands so differently that every brand's operator floor swallows every pairwise distinction — the instrument reports wholesale sub-resolution rather than manufacturing findings (the no-rescue rule), while its diagnostics localize the discordance to a single operator role and its exploratory concordant-triplet analysis shows the predicted metameric structure (half of resolvable distinctions destroyed by the scalar score; the binary pick destroying nearly all; the ranking fewest) below confirmatory strength. The metameric fraction is thereby delivered as an instrument: frozen protocol, measured floors, planted-positive and same-brand-negative controls, seeded estimator, and a concordance diagnostic that tells the consumer of any aggregate metric exactly when the question \"what did this number destroy?\" can and cannot be answered.", "n_prop_claims": 6, "terms": { "owns": [ "aggregator-battery", "garbling-severity-ladder", "metamer-pair", "metameric-fraction", "prism-m" ], "imports": [ "behavioral-metamerism", "coherence-type", "cohort", "dimensional-collapse-index", "incumbent-garbling-operator", "metameric-observer", "operator-noise-floor", "per-pair-resolution-criterion", "prism-five-layer-scaffold", "prism-instrument", "spectral-dimensions", "spectral-metamerism" ], "refines": [] } }, { "key": "2026b", "title": "The Atom-Cloud-Fact Epistemological Pipeline: From Financial Document Processing to Brand Perception Modeling", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.18944770", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/alibi-epistemology", "thesis": "The atom-cloud-fact pipeline is a domain-general epistemological architecture — a formal model of how knowledge forms from heterogeneous observation — not merely a financial document-processing technique. It models knowledge formation through three formally distinct stages: atomic observation (typed, source-bound, immutable data extraction), probabilistic cloud formation (weighted multi-dimensional clustering of revisable hypotheses), and fact collapse (threshold-based crystallization subject to full re-collapse on new evidence). Seven architectural principles (dimensional typing, source binding, identity gating, asymmetric tolerances, weighted scoring, re-collapse, epistemic separation) govern the pipeline and transfer with parametric extension from financial reconciliation to multi-cohort brand perception, where the single-observer assumption is replaced by a heterogeneous-observer model — producing Spectral Brand Theory. The architecture supports four testable propositions about confirmation bias, multi-model replication, epistemic category errors, and cross-model disagreement; and it satisfies four requirements (path-independence, observer heterogeneity, epistemic separation, linguistic implementability) that Bayesian updating, AGM revision, Dempster-Shafer theory, and symbolic expert systems each fail structurally on at least one.", "n_prop_claims": 16, "terms": { "owns": [ "atom", "atom-cloud-fact-pipeline", "epistemic-separation", "identity-gate" ], "imports": [ "brand-conviction", "brand-fact", "cohort", "observer-spectral-profile", "perception-cloud", "re-collapse", "spectral-brand-theory" ], "refines": [] } }, { "key": "2026ba", "title": "Separating Instrument Drift from Brand Signal: A Pre-Registered Model-Version Tracking Instrument for AI Brand Perception (PRISM-T)", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.21128779", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/prism-t-version-floor", "thesis": "Every longitudinal claim made with an LLM-observer instrument is confounded by the instrument itself: when a brand's eight-dimension reading moves between epochs, either the brand's public signal changed or the vendor shipped a model version that reads the same artifacts differently — and practice cannot tell the two apart. PRISM-T resolves the confound with a two-panel identification strategy: a pinned panel (public artifacts captured once, hash-sealed, byte-identical at every reading — so ALL movement is apparatus drift) and a live panel (fresh artifacts each epoch — apparatus drift PLUS brand signal), yielding a version floor that extends the operator floor of the Brand Spectrometer from a same-time cross-model band to an across-time cross-version band, with the no-rescue nesting rule (operator inside version) making \"the brand moved\" a claim that must clear the version floor. The instrument is grounded metrologically — the version floor is classical test-retest dispersion with the locus of error inverted from respondent to apparatus, a non-parametric bound on longitudinal measurement non-invariance, and the mirror image of concept-drift monitoring (data fixed by construction, model moving) — and delivered empirically at epoch VE-1 across three real shipped version ladders (five Anthropic Opus versions, three OpenAI snapshots spanning eighteen months, three Alibaba Qwen releases) read against a sealed 160-artifact panel under cross-family operator pairs, with a same-version negative control, a designated distant-pair positive control, a pre-registered mechanical operator-exclusion rule that replicated the known discordant renderer a third time, and a simulation power analysis that fixes ex ante what drift magnitude the design can certify. Both outcomes are results: drift makes the version floor mandatory equipment for longitudinal LLM measurement; the null makes version-robustness a measured, citable property with an interval rather than an assumption.", "n_prop_claims": 6, "terms": { "owns": [ "live-panel", "pinned-panel", "prism-t", "version-epoch", "version-floor" ], "imports": [ "artifact-noise-floor", "coherence-type", "floor-nesting", "operator-noise-floor", "per-pair-resolution-criterion", "prism-five-layer-scaffold", "prism-instrument", "reflection", "spectral-dimensions", "substrate-floor" ], "refines": [] } }, { "key": "2026bb", "title": "From Stated Perception to Revealed Choice: A Pre-Registered Instrument for the Choice-Perception Gap in AI Brand Perception (PRISM-C)", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.21128342", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/prism-c-choice", "thesis": "What an AI observer says about brands does not predict what it does when it chooses among them — and the size and structure of that wedge is measurable, not assertable. PRISM-C measures the choice-perception gap: the rate at which a model's revealed pick in a simulated agentic choice task diverges from the pick its own stated eight-dimension readings predict, evaluated against the choice elicitation's own cross-family operator floor. The pre-registered campaign returns an unusually clean verdict: four chooser families are near-unanimous with one another (mean within-scenario pick unanimity.972; choice floor.044) yet diverge from the cosine-predicted pick on.633 of 1,144 trials — a gap fourteen times the instrument's noise floor, surviving counterbalancing, threshold and metric alternates, and both controls. The dimensional choice-weight model localizes the wedge: choice weights the stated dimensions unequally, with sign reversals, and a pre-registered mechanism battery rules out presentation order and tie-breaking noise while implicating a systematic brand-level choice policy the stated profile only partially carries. The practical payload is a validity bound the agentic-commerce era needs: perception-level measurement does not transfer to choice-level prediction for free, and the gap between them is now an instrument-measured quantity with controls and floors rather than an anecdote.", "n_prop_claims": 6, "terms": { "owns": [ "choice-operator-floor", "choice-perception-gap", "dimensional-choice-weights", "need-vector", "prism-c" ], "imports": [ "coherence-type", "cohort", "metameric-observer", "operator-noise-floor", "perception-dop", "prism-b", "prism-five-layer-scaffold", "prism-instrument", "spectral-dimensions" ], "refines": [] } }, { "key": "2026bc", "title": "The Producer-Observer Seam: Joining Spectral Brand Theory and Organizational Schema Theory at Meaning, Meaningfulness, and the Perception Cloud", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.21114525", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/producer-observer-seam", "thesis": "The corpus's two flagship frameworks already draw the same line from opposite sides without naming it: Organizational Schema Theory terminates at the rendered Tier-4 instance and hands off to the observer perceptual filter, while the meaning/meaningfulness framework's pipeline (substrate -> meaning S -> rendered instance R -> observer projection -> perception cloud) begins its observer half exactly where the tier stack stops. This note makes the seam explicit: OST owns the producer side (substrate -> S -> R, Tiers 1-4), SBT owns the observer side (R -> perception cloud), and the meaning/meaningfulness/perception triad is a JOIN of the two frameworks, not a slice of either alone. Three results follow. First, the seam map with two honesty guards (meaningfulness is multi-tier in general; perception is definitionally outside the tier stack). Second, a flattening parametrization: the triad attaches to whatever tier a business's value concentrates toward, with software (Process and Organization tiers approaching zero) as the limit existence proof. Third, an endogenous-intent closure: perception clouds sediment into the next generation's substrate through human transducers, making Tier-1 intent a fixed point of a human-mediated loop rather than an exogenous primitive - with a measurable shadow (perception-cloud variance over time as the loop-health diagnostic) that connects machine-observer dimensional collapse to model-collapse and output-homogenization results.", "n_prop_claims": 6, "terms": { "owns": [ "levels-of-reading", "observer-depth", "perception-cloud-as-foam" ], "imports": [ "cohort", "observer-spectral-profile", "perception-cloud" ], "refines": [] } }, { "key": "2026c", "title": "Geometric Approaches to Brand Perception: A Critical Survey and Research Agenda", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.18945217", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r0-literature-survey", "thesis": "Brand theory is strikingly under-formalized relative to adjacent fields where geometric methods have produced transformative insight. Across ten intellectual traditions — multidimensional scaling, characteristics-space economics, conceptual spaces, non-Euclidean perceptual geometry, information geometry, individual-differences scaling, topological data analysis, quantum cognition, opinion dynamics, and non-ergodicity research — no single framework simultaneously combines high-dimensional geometric structure, a formal metric, observer heterogeneity, non-ergodic temporal dynamics, and a generative signal mechanism. This compound gap is not a single missing ingredient but the absence of the five ingredients in combination. The survey maps the genealogy, diagnoses the gap via a classification matrix, and articulates six open problems with formal mathematical statements that constitute a research agenda for mathematical brand theory. Spectral Brand Theory (Zharnikov 2026a) is positioned as a candidate framework sitting at the five-way intersection, with companion papers (Zharnikov 2026d–h, 2026j) delegated to resolve each open problem.", "n_prop_claims": 16, "terms": { "owns": [ "compound-gap" ], "imports": [ "absorbing-state", "cohort", "non-ergodic-perception", "observer-spectral-profile", "perception-cloud", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026d", "title": "Brand Space Geometry: A Formal Metric for Multi-Dimensional Brand Perception", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.18945295", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r1-formal-metric", "thesis": "Brand theory has lacked a rigorous distance function capable of quantifying perceptual closeness while respecting the compositional, relative, and observer-dependent nature of consumer attention. This paper constructs the first observer-warped metric space for multi-dimensional brand perception, grounding it in Cencov's uniqueness theorem and compositional data analysis. Three metric spaces are defined: the brand signal space (the positive orthant R^8_+ with the Aitchison metric, justified by Weber-Fechner scaling and subcompositional coherence), the observer weight space (the probability simplex Delta^7 with the Fisher-Rao metric, uniquely invariant under Markov morphisms by Cencov), and a warped product combining them so that brand distance becomes observer-dependent, generalizing the empirically validated INDSCAL model. Metric axioms are proved and geodesics derived for each. Concentration-of-measure analysis at eight dimensions supplies a null baseline of approximately.44 for observer pairwise distance; the positive-octant restriction compresses brand space to 1/256 of the full 7-sphere; and Jacobi-field analysis yields a spectral sensitivity index that links static geometry to dynamic trajectory vulnerability, with singularities at structural-absence boundaries. The central result is that brand distance is not an objective property of brands but a function of the observer's attentional structure: different observer cohorts inhabit metrically distinct brand landscapes. This supplies the mathematical foundation for differentiation measurement, cohort definition, and positioning optimization, resolving Problem 1 of the accompanying geometric survey (2026c).", "n_prop_claims": 12, "terms": { "owns": [ "brand-signal-space", "observer-weight-space", "spectral-sensitivity-index" ], "imports": [ "cohort", "non-ergodic-perception", "observer-spectral-profile", "re-collapse", "spectral-brand-theory", "spectral-dimensions", "structural-absence" ], "refines": [] } }, { "key": "2026e", "title": "Spectral Metamerism in Brand Perception: Projection Bounds from High-Dimensional Geometry", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.18945352", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r2-spectral-metamerism", "thesis": "Scalar brand metrics compress an eight-dimensional perceptual signal into a single number, and the information cost of that compression is a geometric inevitability, not an implementation detail. Spectral metamerism — structurally distinct brand profiles that produce identical scalar evaluations — is the brand-perception analogue of metamerism in colour science: the projection from R^8_+ to R^1 (SBT's L1-to-L2 grade map) creates a 7-dimensional null space of invisible profile differences. Three independent lines of argument converge: (1) the Johnson-Lindenstrauss lower bound forces distortion exceeding 152% for 10 brands and 198% for 50 under any 1D projection; (2) the rank-nullity theorem guarantees a 7-dimensional family of metameric profiles for every grade; and (3) an information-theoretic channel bound caps a 5-level grade at 2.32 bits of a ~20-bit profile, ~11.6% retention. Monte Carlo simulation confirms 31--39% of well-separated brand pairs collapse to metameric coincidence under a random 1D projection. The practical consequence is the distinction between rasterized brand management (a human operator lossily projecting the full specification through cognitive and communicative bottlenecks) and vectorized brand management (the full eight-dimensional spectral profile as single source of truth, with channel outputs computed as projections of known, bounded loss).", "n_prop_claims": 10, "terms": { "owns": [ "rasterized-vectorized-brand-management", "spectral-metamerism" ], "imports": [ "cohort", "observer-spectral-profile", "perception-cloud", "spectral-brand-theory", "spectral-dimensions", "structural-absence" ], "refines": [] } }, { "key": "2026f", "title": "Geometric Necessity of Fuzzy Cohort Boundaries: A Concentration Analysis of the 7-Simplex", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.18945477", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r3-cohort-boundaries", "thesis": "In the eight-dimensional probability simplex Delta^7 that serves as Spectral Brand Theory's observer weight space, the fuzziness of perceptual cohort boundaries is not a measurement artifact, an algorithmic limitation, or an empirical curiosity — it is a geometric necessity under the uniform Dirichlet(1,...,1) null. Concentration of measure forces (i) pairwise distances to concentrate around their mean, degrading the distance contrast ratio to ~7.5 at n=8 (a transitional regime: clustering is informative but noisy); (ii) at least 52.2% of Delta^7 to lie within relative distance delta=.10 of ANY convex partition boundary, so a majority of observer profiles sit near a cohort boundary and discrete assignment is inherently unstable; and (iii) Levy concentration on S^7 to bound 1-Lipschitz deviations. Monte Carlo with 10^5 draws confirms the bounds within sampling error. The uniform null is the WORST case: symmetric Dirichlet(alpha,...,alpha) with alpha>=3 reduces the boundary fraction by alpha^{-7/2}, producing operationally crisp boundaries (below 2%) for empirically plausible alpha. Together these give a geometric foundation for preferring continuous observer profiles (\"vectorized\") over discrete cohort labels (\"rasterized\") once perceptual dimensionality exceeds five, and define a capacity-resolution duality dual to the R4 sphere-packing bound.", "n_prop_claims": 14, "terms": { "owns": [ "boundary-volume-fraction" ], "imports": [ "absorbing-state", "cohort", "non-ergodic-perception", "observer-spectral-profile", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026g", "title": "How Many Brands Can a Market Hold? Sphere Packing Bounds for Multi-Dimensional Positioning", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.18945522", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r4-sphere-packing", "thesis": "Brand perception in Spectral Brand Theory is formalized as points in the positive orthant R^8_+ under the Aitchison metric, which the centered log-ratio transform renders isometric to Euclidean distance on a 7-dimensional hyperplane, so the question \"how many distinguishable brand positions can a market sustain?\" maps exactly onto sphere packing in eight dimensions. Because the E_8 lattice is the proved optimal packing in R^8 (Viazovska 2017) — packing density pi^4/384 ~.2537, kissing number 240 — it supplies structural ceilings: positioning capacity is at least (1/epsilon)^8 (10^8 distinguishable positions at epsilon =.10), each position has at most 240 nearest competitors decomposing into 112 specialist and 128 generalist vectors, 10,000 brands occupy under.01% of the unit 8-ball, category saturation occurs near (1/epsilon)^d_eff, and average inter-dimension correlation rho =.3 collapses effective dimensionality to ~2.6 and capacity by roughly five orders of magnitude. The E_8 connection is structural, not literal — a ceiling on positioning order, not a claim that brands sit on lattice points. An LLM stability experiment (250 calls, five models) finds null competitive-interference effects, supporting the fixed-geometry assumption on which the bounds rest.", "n_prop_claims": 10, "terms": { "owns": [ "perceptual-threshold", "positioning-capacity" ], "imports": [ "cohort", "observer-spectral-profile", "spectral-brand-theory", "spectral-dimensions", "structural-absence" ], "refines": [] } }, { "key": "2026h", "title": "Specification Impossibility in Organizational Design: A High-Dimensional Geometric Analysis", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.18945591", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r5-specification-impossibility", "thesis": "Comprehensive organizational specification is geometrically impossible. OrgSchema Theory's 8×6 activation matrix is formalized as a 48-dimensional specification space [0,1]^48, and three closed-form results follow. (1) Coverage Impossibility: at resolution epsilon = 0.1 per dimension the space admits 10^48 distinguishable specifications, each covering a ball of volume V_48(0.1) ≈ 1.38e-60, so even 10^20 templates cover only ~10^-40 of the space. (2) Effective Dimensionality Reduction: OST's cascade model collapses effective dimensionality from 48 to d_eff = 8(1-(1-gamma)^6)/gamma, i.e. 15.75 at gamma = 0.5 (a 67% reduction), making per-organization specification tractable without making the space coverable. (3) Forkability as Subspace Decomposition: the fork model partitions [0,1]^48 into a shared and a private subspace (24+24 at the canonical k=3 fork), formalizing franchises, open-source ecosystems, and denominational structures. An information-theoretic reading shows a full specification carries 159.4 bits — far above human working-memory capacity — so cascade and fork compression is cognitively necessary, not merely convenient. The results are strictly complementary to Simon's bounded rationality and to NK landscape search complexity: geometric impossibility holds regardless of cognitive capacity or any fitness function.", "n_prop_claims": 13, "terms": { "owns": [ "activation-matrix", "coverage-impossibility", "effective-dimensionality-reduction", "forkability-decomposition" ], "imports": [ "six-tier-ontology", "spectral-dimensions" ], "refines": [] } }, { "key": "2026j", "title": "Non-Ergodic Brand Perception: Diffusion Dynamics on Multi-Dimensional Perceptual Manifolds", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.18945659", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r6-diffusion-dynamics", "thesis": "An observer's brand conviction can be modeled as a stochastic process on S^7_+ — the positive octant of the 7-sphere — the natural state space for a normalized eight-dimensional observer spectral profile. Signal encounters drive Brownian motion on the manifold, signal decay introduces drift toward a neutral prior, and negative conviction creates absorbing Dirichlet boundaries where a perceptual dimension collapses to zero (re-collapse). A Stratonovich SDE on S^7_+ is well-posed up to absorption (Theorem 1); survival probability decays exponentially at rate lambda_{D,1} sigma_0^2 / 2 with exact first Dirichlet eigenvalue lambda_{D,1} = 112 (Theorem 2); the Dirichlet spectral gap lambda_{D,2} - lambda_{D,1} = 48 yields faster mixing to the quasi-stationary distribution than on the full sphere (Theorem 3); and time averages diverge from ensemble averages with probability 1, establishing non-ergodicity through an absorbing-boundary mechanism independent of Peters' (2019) multiplicative framing (Theorem 4). Applied to five case-study brands, absorption risk nearly matches SBT coherence grading with a single inversion explained by coherence-type-dependent drift (Proposition 7); recovery time from a near-death dimension scales as 1/delta^2 (Proposition 5); and a sensitivity analysis recovers the empirically observed D/A Goldilocks zone r* in [.55,.65] from the absorption-exploration tradeoff (Proposition 6). The model gives SBT its missing dynamical foundation and formalizes the distinction between vectorized and rasterized brand management.", "n_prop_claims": 11, "terms": { "owns": [ "brand-perception-sde" ], "imports": [ "absorbing-state", "brand-conviction", "cohort", "d-a-ratio", "ergodicity-coefficient", "non-ergodic-perception", "observer-spectral-profile", "perception-cloud", "re-collapse", "spectral-dimensions" ], "refines": [] } }, { "key": "2026k", "title": "Spectral Resource Allocation: Demand-Driven Investment in Multi-Dimensional Brand Space", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19009268", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r7-spectral-resource-allocation", "thesis": "Brand managers allocate operational resources across perceptual dimensions — design, storytelling, pricing, heritage — yet rarely ground those decisions in measured cohort salience weights. Modeling a brand's signal portfolio s in R^8_+ as evaluated by observer cohorts whose weight vectors w(c) lie on the probability simplex Delta^7, with perceived value the inner product net of a separable convex cost, yields a closed-form optimal allocation (invest in proportion to cohort weight over marginal cost) that generalizes Dorfman–Steiner to eight perceptual dimensions. The central construct is the alignment gap: the economic loss incurred when the portfolio is optimized for the founder's spectral profile rather than the cohort's, which is bounded below by the Fisher–Rao distance between the two weight vectors — giving \"product-market fit failure\" a geometric floor that improved execution cannot recover, only reallocation toward the cohort's measured weights closes it. The framework further characterizes when one portfolio efficiently serves multiple cohorts (a Fisher–Rao ball of radius r < pi/4), reads spectral metamerism as cost minimization (the cheapest portfolio achieving a target perception), and extends the two-media synergy model to a cohort-dependent interaction matrix W(c). It supplies the optimization layer missing from current brand-tracking systems: a diagnostic (alignment audit) and a prescriptive tool (dimension-specific budget ratios). The numerical examples are illustrative, not empirically measured.", "n_prop_claims": 14, "terms": { "owns": [ "alignment-gap", "concentration-premium" ], "imports": [ "cohort", "observer-spectral-profile", "perception-cloud", "spectral-dimensions", "structural-absence" ], "refines": [] } }, { "key": "2026m", "title": "The Projection Cascade: Why Reorganizations Fail When the Specification Cascade Doesn't", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19145205", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/projection-paper", "thesis": "Most strategic reorganizations fail to deliver expected performance gains because they intervene at the org-chart surface (T_6), and interventions there achieve effect-sizes geometrically smaller than interventions at deeper tiers — each deeper tier carries content already compressed in transit to the surface. Organizations are formalized as a six-tier projection cascade linking owner intent (T_1), business model (T_2), governance (T_3), architecture (T_4), routines (T_5), and positions (T_6), where each junction is a rank-reducing linear operator Pi_{i->i+1} with rank deficiency r_i >= 0. A unique cascade-equilibrium exists under tier-by-tier Banach contractions (Theorem 1); total information loss is bounded by the sum of local nullities, with equality only when kernels stack independently (Corollary 1). Five major design theories — Galbraith's star, Williamson's governance choice, Mintzberg's configurations, Puranam's microstructure, and Burton-Obel-Hakonsson's computational optimization — are recovered as nested cascade restrictions, so the field's apparent fragmentation is a partial-view artifact rather than ontological disagreement. A position triple p = (P_p, A_p, R_p) decomposes any T_6 position into perceptual content from T_5, authority from T_3, and role expectation from T_1. The apparatus entails four falsifiable propositions (P1 cascade-distance scaling, P2 strict downward propagation of basis rotation under AI deployment, P3 variance amplification, P4 algebraic decoupling) that no single tradition derives in isolation.", "n_prop_claims": 14, "terms": { "owns": [ "cascade-equilibrium", "position-triple", "projection-cascade" ], "imports": [ "non-ergodic-perception", "six-tier-ontology" ], "refines": [] } }, { "key": "2026n", "title": "From Brand Identity to Spectral Identity: Formalizing Aaker's Framework for Testable, AI-Operable Brand Analysis", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.20741256", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/spectral-identity", "thesis": null, "n_prop_claims": 0, "terms": { "owns": [ "spectral-identity", "spectral-weight" ], "imports": [ "brand-conviction", "cohort", "observer-spectral-profile", "perception-cloud", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026o", "title": "From Order Effects to Absorbing States: A Non-Ergodic Framework for Multi-Dimensional Brand Perception Dynamics", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19138860", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r9-nonergodic-perception", "thesis": "Brand perception is non-ergodic: the time average of an individual observer's brand perception does not converge to the cross-sectional (ensemble) average across observers. Drawing on Peters' (2019) ergodicity framework from statistical physics, three structural sources produce the divergence — absorbing states from deeply negative brand conviction, multiplicative (rather than additive) signal-update dynamics, and path-dependent dimension weighting. Five formal propositions follow: signal order produces structurally different perception profiles from identical signals (P1); negative conviction is an absorbing state while positive conviction is not (P2); cross-sectional brand tracking systematically overestimates brand health for absorption-risk brands via survivorship bias (P3); the first signal in a dimension persistently anchors all subsequent updates (P4); and observer cohorts with different dimension weights diverge permanently under identical signals (P5). These propositions unify roughly eighty years of scattered order-effect, primacy, and belief-updating evidence within Spectral Brand Theory's eight-dimensional perception space, and the bias direction and magnitude are predictable from brand coherence. The framework is scoped to high-involvement B2C brand perception under multiplicative update dynamics.", "n_prop_claims": 11, "terms": { "owns": [ "absorbing-state", "ergodicity-coefficient", "non-ergodic-perception" ], "imports": [ "cohort", "perception-cloud" ], "refines": [] } }, { "key": "2026p", "title": "Dimensional Activation and Cohort Divergence: A Longitudinal Decomposition of Purpose Advertising Effectiveness", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19139258", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r10-dove-case-study", "thesis": "Purpose campaigns are evaluated by aggregate metrics that cannot distinguish structural success from surface popularity. Applying the SBT eight-dimension decomposition to Dove's \"Campaign for Real Beauty\" (2004–2026) across four temporal cross-sections shows that the campaign's disproportionate commercial impact is traceable to dimensional creation — the activation of a previously null Ideological dimension that opens new perceptual territory rather than competing within existing space. Four observer cohorts (Purpose-Aligned, Product-Pragmatist, Social-Signal Reader, Skeptic-Critic) receive identical signals but form structurally different brand convictions, with Purpose-Aligned and Skeptic-Critic forming a mirror pair (near-identical weight vectors, opposite conviction valence). Five propositions generalize the case: dimensional creation, observer heterogeneity, portfolio spectral interference, counter-cultural decay, and dimensional specificity over intensity. Independent AI-observer evidence (2026v) replicates the cohort-divergence and Patagonia-as-exception patterns, anchoring the interpretive case in a controllable observer population.", "n_prop_claims": 7, "terms": { "owns": [ "counter-cultural-decay", "dimensional-creation", "portfolio-spectral-interference" ], "imports": [ "brand-conviction", "cohort", "observer-spectral-profile", "perception-cloud", "spectral-brand-theory", "spectral-dimensions", "structural-absence" ], "refines": [] } }, { "key": "2026r", "title": "Why Eight? Completeness and Necessity of the SBT Dimensional Taxonomy", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19207599", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r11-dimension-justification", "thesis": "Every multi-dimensional brand theory must justify its dimensional count, yet existing frameworks diverge widely (five personality factors, six prism facets, two-to-three MDS solutions) without theoretical warrant for the number chosen. This paper derives the SBT eight-dimensional taxonomy — semiotic, narrative, ideological, experiential, social, economic, cultural, temporal — from first principles, treating each dimension as a distinct MEANING CHANNEL rooted in an independent academic tradition rather than an empirically discovered factor. Independence is shown via counter-example brand pairs that differ on one channel while matched on the others; non-redundancy because removing any channel collapses discriminative power for at least one pair; completeness because five candidate ninth dimensions (aesthetic, functional, ethical, digital, environmental) each reduce to combinations of existing channels or to content domains processed through them. The apparent conflict with low-dimensional MDS is resolved via concentration of measure: low-dimensional projections capture most variance while discarding the profile-shape information that distinguishes coherence types. An empirical robustness test on R15 cross-cultural LLM data confirms every dimension carries non-trivial cross-model variance (5–19%) and that ranking stability deteriorates below eight dimensions. The argument is theoretical and motivates, but does not replace, future human-subject factor-analytic validation.", "n_prop_claims": 13, "terms": { "owns": [ "meaning-channel", "meaning-channel-vs-content-domain" ], "imports": [ "cohort", "observer-spectral-profile", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026s", "title": "Coherence Type Over Coherence Score: A Stochastic Differential Equation Derivation of Brand Resilience", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19208107", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r12-coherence-resilience", "thesis": "Spectral Brand Theory's qualitative prediction — that coherence TYPE (the geometric pattern of emission across the eight perceptual dimensions) predicts crisis resilience better than coherence SCORE (total emission intensity) — is here derived formally from the drift geometry of the Stratonovich SDE on the positive orthant of the 7-sphere developed in Zharnikov (2026j). Different coherence types produce different signal-driven drift fields alpha_i = gamma * s_i * x_i; characterizing those fields by drift isotropy and k-anisotropy yields three theorems: absorption probability decreases monotonically in drift isotropy (Theorem 1), recovery probability depends on dimension-specific drift creating asymmetric vulnerability profiles (Theorem 2), and the full resilience ordering ecosystem > signal > identity > experiential asymmetry > incoherent follows from SDE geometry (Theorem 3). The central type-over-score principle is that crisis survival depends on the MINIMUM drift across dimensions (the weakest link), not the average, so two brands with identical total emission but different distributions have different resilience. The framework is applied to four documented crises and generates three falsifiable predictions.", "n_prop_claims": 11, "terms": { "owns": [ "coherence-type", "drift-isotropy", "ecosystem-coherence", "experiential-asymmetry", "identity-coherence", "incoherent-coherence", "signal-coherence", "type-over-score-principle" ], "imports": [ "absorbing-state", "brand-conviction", "non-ergodic-perception", "observer-spectral-profile", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026u", "title": "Research as Repository: Infrastructure for Transparent, Attributed, and Machine-Readable Scholarly Communication", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19294864", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r14-paper-as-repository", "thesis": "Scientific publishing is the only knowledge-intensive domain without formal version-control and provenance infrastructure. Treating every research program as a version-controlled repository — of which a paper is a render at a point on its timeline, a submission a fork, peer review attributed commits on a review branch, and publication a merge — closes five persistent structural gaps (no version history, no contributor traceability, no submission provenance, no review attribution, no machine interface) without replacing peer review or mandating a centralized platform. The protocol optimizes the knowledge-production process, not the rendered paper. As of the 2026-06-13 revision the protocol is no longer only a proposal: the author's own corpus runs a working instantiation — a single content-addressed substrate unifying terms, claims, and citations, a link-time compatibility checker that treats each paper as a module in a typed codebase, and a CI-style anti-drift gate — which is an existence proof of the repository reconception on a live body of work. The strong claim (a new mode of scholarly communication) is warranted as an existence proof and design; full validation requires multi-author adoption and an explicit negotiation protocol, which are future work.", "n_prop_claims": 11, "terms": { "owns": [ "anti-drift-gate", "bundle-as-render", "commit-reveal-priority", "link-time-compatibility-check", "peer-alignment-event", "research-as-repository", "substrate-as-repository" ], "imports": [ "six-tier-ontology", "spectral-brand-theory", "spine", "spine-first-drafting-protocol" ], "refines": [] } }, { "key": "2026v", "title": "Dimensional Collapse in AI-Mediated Search: Large Language Models as Metameric Observers of Brand Advertising", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19422427", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r15-ai-search-metamerism", "thesis": "Large language models increasingly mediate consumer brand evaluation in search and agentic commerce, and they act as metameric observers: they systematically collapse the eight-dimensional brand emission profile toward the verifiability anchors (Economic and Semiotic, with Experiential inflated separately), rendering brands differentiated on Narrative, Ideological, Cultural, or Temporal dimensions structurally different but functionally equivalent in AI recommendations. Measured with the PRISM-B forced-allocation instrument across 21,350 API calls to 24 models from nine cultural traditions and 15 languages, the Dimensional Collapse Index (uniform baseline =.250) is elevated (mean.294 global,.356 cross-cultural) and convergent across architectures (cosine.977), so the collapse is structural rather than a platform quirk. Collapse is conditional on training-data embeddedness — locally embedded brands collapse about 24% more — and partially recoverable (~20% of lost dimensionality) by encoding soft dimensions as verifiable, machine-readable Brand Function specifications. For search advertising this reframes strategy from platform selection to dimensional defensibility: advertisers must encode soft brand dimensions in machine-readable form or risk effective erasure by LLM intermediaries. The findings are bounded to the text-conditioned LLM observers tested here.", "n_prop_claims": 9, "terms": { "owns": [ "dimensional-collapse", "dimensional-collapse-index", "metameric-observer" ], "imports": [ "brand-conviction", "cohort", "observer-spectral-profile", "perception-cloud", "prism-b", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026w", "title": "Canon as Repository: A Specification-Driven Architecture for Transmedia Intellectual Property", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19355800", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/canon-as-repository", "thesis": "Creative intellectual property management is the only mature domain of complex designed systems that lacks a formal consistency-verification construct: engineering, medicine, financial auditing, software, and scientific publishing each independently developed mechanisms to verify that artifacts satisfy their specifications, but creative IP has not. Transmedia franchises accumulate contradictions across novels, films, games, and merchandise because no formal specification governs what a story IS independently of how it is expressed. This is an instance of the rendering problem: a specification of bounded complexity (the canon) is rendered into an implementation of vastly greater complexity (medium-specific expression), producing an emergent layer (audience perception) that the specification does not contain. The paper proposes that the canon be reconceived as a version-controlled repository — editions are tagged commits, translations and adaptations are forks, canon governance is pull requests, and consistency validation is continuous integration — with style as a rendering parameter, actors and translators as rendering operators, and AI clarifying authorship by distinguishing specification (the creative act) from rendering (the craft act). The contribution is the GAP (creative IP lacks the construct), not the TOOL (Git is one instrumental implementation among possible ones).", "n_prop_claims": 15, "terms": { "owns": [ "audience-as-renderer", "canon-as-repository" ], "imports": [ "perception-cloud", "research-as-repository", "spectral-brand-theory" ], "refines": [] } }, { "key": "2026x", "title": "AI-Native Brand Identity: From Visual Recognition to Cryptographic Verification", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19391476", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r16-ai-native-brand-identity", "thesis": "Brand identity verification technology changes discontinuously whenever the primary observer type changes: wax seals, hallmarks, trademarks/logos, and SSL certificates each emerged in response to a new observer class. The sixth observer is the text-primary AI purchasing agent, which evaluates brands through structured data, behavioral signals, and third-party corroboration rather than visual recognition, giving the logo near-zero informational weight. The Brand Function — f(query, context, observer_type, time) -> response — is the root behavioral specification AI observers require; cryptographic signatures on this specification are predicted to replace logos as the primary identity mechanism for machine observers. The framework names a new failure mode, behavioral metamerism: brands that converge on statistically indistinguishable profiles (especially under generative engine optimization) while differing in structurally relevant behavioral contingencies, an observational equivalence that statistical optimization cannot resolve and that only access to the structural specification breaks. The paper is conceptual, advances six falsifiable propositions, and is scoped to B2C text-primary agentic commerce.", "n_prop_claims": 8, "terms": { "owns": [ "behavioral-metamerism", "brand-function", "observer-driven-evolution-thesis" ], "imports": [ "brand-conviction", "metameric-observer", "observer-spectral-profile", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026y", "title": "Brand Triangulation: A Geometric Framework for Multi-Observer Brand Positioning", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19482547", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r17-brand-triangulation", "thesis": "The multi-observer heterogeneity that contemporary brand measurement treats as a nuisance is, when decomposed into structural differences in observer spectral weight profiles, the primary source of positioning information. Mapping observer cohorts to GPS satellites, the brand emission profile to receiver location, and systematic cohort bias to receiver clock error, brand-spectral-profile estimation from multiple cohorts is a weighted least-squares positioning problem. The framework introduces Perception DOP (PDOP) — a scalar computed solely from proposed cohort weight profiles that bounds estimation precision before any data are collected — differential brand measurement using reference brands to cancel systematic observer bias, and identifiability conditions linking spectral metamerism to geometric underdetermination. PDOP's predictive validity is confirmed by Monte Carlo simulation, and the geometry is demonstrated on a six-LLM observer constellation; together these upgrade brand measurement from opinion aggregation to geometric estimation.", "n_prop_claims": 13, "terms": { "owns": [ "brand-triangulation", "differential-brand-measurement", "perception-dop" ], "imports": [ "brand-conviction", "cohort", "observer-spectral-profile", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } }, { "key": "2026z", "title": "Spectral Dynamics: Velocity, Acceleration, and Phase Space in Multi-Dimensional Brand Perception", "status": "active", "doi_url": "https://doi.org/10.5281/zenodo.19468204", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r18-spectral-dynamics", "thesis": "Brand tracking routinely measures static perceptual position but rarely quantifies trajectory. Extending Spectral Brand Theory's eight-dimensional perception space from static profiles to a formal differential calculus, this paper defines brand velocity (the drift of the perception state) and acceleration as vector quantities in R^8 and a 16-dimensional phase space pairing position and velocity. Three theoretical results follow. First, velocity resolves a metric-ambiguity (Bonnet-pair-analogous) problem: brands with identical spectral profiles but different velocities are distinguishable in phase space and provably diverge under the SBT diffusion dynamics. Second, a directional-coherence metric quantifies alignment between a brand's actual trajectory and its a-priori strategic intent. Third, trajectory clustering groups brands by dynamic state rather than static position, enabling detection of competitive convergence/divergence before it manifests in position. The framework promotes velocity from an instrumental Kalman-filter state component to a first-class theoretical quantity, embedding existing state-space marketing models within a unified kinematic theory. It is illustrated (not validated) on author-assigned Dove profiles across four strategic periods (2003-2023).", "n_prop_claims": 12, "terms": { "owns": [ "brand-acceleration", "brand-phase-space", "brand-velocity", "directional-coherence", "spectral-dynamics", "trajectory-clustering" ], "imports": [ "absorbing-state", "cohort", "non-ergodic-perception", "observer-spectral-profile", "perception-cloud", "spectral-brand-theory", "spectral-dimensions" ], "refines": [] } } ], "terms": [ { "key": "absorbing-state", "label": "absorbing state", "owner": "2026o", "definition": "An irreversible negative-conviction basin: a cohort state from which the perception cloud cannot recover under ordinary signal emission.", "papers": { "owns": [ "2026o" ], "imports": [ "2026ad", "2026ai", "2026c", "2026f", "2026j", "2026s", "2026z" ], "refines": [] }, "relations": [] }, { "key": "activation-matrix", "label": "Activation Matrix", "owner": "2026h", "definition": "The $8\\times 6$ matrix $A \\in [0,1]^{8\\times 6}$ whose entry $A_{ij}$ is the activation level of spectral dimension $i$ at organizational level $j$, vectorizable to a point in the 48-dimensional specification space.", "papers": { "owns": [ "2026h" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "aggregator-battery", "label": "Aggregator battery", "owner": "2026az", "definition": "The three coarse readouts PRISM-M tests as garbling operators, each matched to a real consumption surface and each carrying its OWN measured noise floor: A-SCORE (a single brand-health grade mapped to [0,1]; the scalar scorecard surface), A-RANK (position in a ten-slot recommendation ranking; the AI-search surface), and A-PICK (a binary recommend/do-not-recommend call; the agentic recommendation surface). Formalized as projection operators of the full eight-dimension readout.", "papers": { "owns": [ "2026az" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "agreement-class", "label": "AGREEMENT", "owner": "federated-negotiation", "definition": "The interaction class where both authors own the same term_key with identical def_hash; resolved; SKOS exactMatch; reconciliation operation MERGE (either author may import the other's term unchanged).", "papers": { "owns": [ "2026at" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "interaction-class" } ] }, { "key": "alignment-gap", "label": "Alignment Gap", "owner": "2026k", "definition": "The economic value loss incurred when a brand's signal portfolio is optimized for the founder's spectral weight profile rather than the target cohort's, bounded below by the Fisher-Rao distance between the two weight profiles on the probability simplex.", "papers": { "owns": [ "2026k" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "anti-drift-gate", "label": "Anti-drift gate", "owner": "2026u", "definition": "A continuous-integration-style check run after every paper edit and before commit that fails the build when a paper drifts from its companion artifacts (citations, ontology module, claim graph) or when a dangling import, incompatible refinement, or definitional drift appears in the linked corpus.", "papers": { "owns": [ "2026u" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "append-only-organizational-log", "label": "Append-only organizational log", "owner": "2026al", "definition": "A partially ordered set of immutable, typed events (decisions, failures, policies, personnel, artifacts) recording everything a firm has actually done, serving as the substrate beneath capability.", "papers": { "owns": [ "2026al" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "artifact-noise-floor", "label": "Artifact-noise floor", "owner": "2026ax", "definition": "The instrument-computed convergent-validity floor for a cohort: the maximum cosine distance between the cohort's primary spec vector and the vectors produced under leave-one-out perturbation of its artifact set, using the primary operators. It quantifies sensitivity of the cohort vector to artifact sampling and is the threshold V3 (split-half) is read against.", "papers": { "owns": [ "2026ax" ], "imports": [ "2026ba" ], "refines": [] }, "relations": [] }, { "key": "atlas", "label": "Atlas", "owner": "2026ax", "definition": "The complete assembled output of the instrument for one brand and one dated sampling window: every cohort vector with its per-dimension computed intervals, the operator and source noise floors, the per-pair distances and signal-to-noise values, and the artifact manifest. The worked example comprises two atlases of one case (a fresh and a pinned window); the published atlas is what V5 re-derives byte-for-byte.", "papers": { "owns": [ "2026ax" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "perception-cloud" } ] }, { "key": "atom", "label": "Atom (typed observation)", "owner": "2026b", "definition": "A typed, source-bound, immutable unit of raw observation belonging to exactly one dimension and exactly one source.", "papers": { "owns": [ "2026b" ], "imports": [ "2026ax" ], "refines": [] }, "relations": [] }, { "key": "atom-cloud-fact-pipeline", "label": "Atom-Cloud-Fact Pipeline", "owner": "2026b", "definition": "A domain-general three-stage epistemological architecture in which knowledge forms through atomic observation (typed, source-bound data), probabilistic cloud formation (weighted multi-dimensional clustering), and fact collapse (threshold-based crystallization with full re-collapse on new evidence).", "papers": { "owns": [ "2026b" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "audience-as-renderer", "label": "The Audience as Renderer", "owner": "2026w", "definition": "The condition in which, once specification and rendering are formally separated and rendering technology is sufficiently capable, observers can generate personalized renderings from a published canonical specification, transforming the author's role from renderer to specifier.", "papers": { "owns": [ "2026w" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "behavioral-metamerism", "label": "Behavioral metamerism", "owner": "2026x", "definition": "The AI-native failure mode in which brands converge on statistically indistinguishable profiles while differing in structurally relevant behavioral contingencies, an observational equivalence that statistical optimization cannot resolve.", "papers": { "owns": [ "2026x" ], "imports": [ "2026az" ], "refines": [] }, "relations": [] }, { "key": "blind-spend", "label": "Blind spend", "owner": "2026au", "definition": "Brand-management effort that an aggregate-score optimizer allocates along perception dimensions its framework projects away, so that its effect on perception and behavior is unobservable to that optimizer — it may help, hurt, or do nothing, and the manager cannot tell which.", "papers": { "owns": [ "2026au" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "boundary-volume-fraction", "label": "Boundary Volume Fraction", "owner": "2026f", "definition": "The fraction of probability mass on the simplex lying within a given relative distance of any convex partition boundary, bounded below at 52.2% for n=8 and delta=.10 under the uniform Dirichlet null, quantifying the geometric instability of discrete cohort assignment.", "papers": { "owns": [ "2026f" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "brand-acceleration", "label": "Brand Acceleration", "owner": "2026z", "definition": "The second time derivative of a brand's spectral profile, $a(t)=d^2x/dt^2$, capturing whether brand movement is intensifying, stabilizing, or reversing.", "papers": { "owns": [ "2026z" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "brand-agnostic-brand-bound-decomposition", "label": "Brand-agnostic / brand-bound tier decomposition", "owner": "2026ah", "definition": "A per-tier partition of each of the six tiers into brand-agnostic subcomponents (shared across brands) and brand-bound subcomponents (specific to one Tier-4 instance) that determines a tier's separability under multi-brand operation.", "papers": { "owns": [ "2026ah" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "brand-as-tier-4-projection", "label": "Brand as Tier-4 projection", "owner": "2026ah", "definition": "The claim that a brand IS the Tier-4 customer-facing product specification surface, not its perception, trademark, or marketing communications.", "papers": { "owns": [ "2026ah" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "brand-conviction", "label": "brand conviction", "owner": "2026a", "definition": "An observer-relative held position about a brand on one or more spectral dimensions. Observer-relative, not dispositional (contrast: attitude).", "papers": { "owns": [ "2026a" ], "imports": [ "2026ac", "2026ah", "2026ai", "2026ar", "2026as", "2026au", "2026b", "2026j", "2026n", "2026p", "2026s", "2026v", "2026x", "2026y" ], "refines": [] }, "relations": [] }, { "key": "brand-fact", "label": "brand fact", "owner": "2026a", "definition": "A brand conviction treated as a held fact in an observer's perception. Interchangeable with brand conviction; \"conviction\" is preferred in papers.", "papers": { "owns": [ "2026a" ], "imports": [ "2026b" ], "refines": [] }, "relations": [ { "type": "synonym", "target": "brand-conviction" } ] }, { "key": "brand-function", "label": "Brand Function", "owner": "2026x", "definition": "A root specification concept defined as f(query, context, observer_type, time) -> response, constituting the complete machine-readable behavioral specification a brand provides for machine observers, integrating spectral perception dimensions, observer-contingent decision rules, and computable coherence metrics.", "papers": { "owns": [ "2026x" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "brand-management-correspondence-theorem", "label": "Brand-management correspondence theorem", "owner": "2026au", "definition": "The result that an incumbent aggregate brand-health score is a sufficient statistic for the managerial decision problem — so the incumbent framework and Spectral Brand Theory prescribe the same optimal action for every payoff — if and only if four regime conditions hold jointly (a tight unimodal perception cloud, slow temporal dynamics, a human-only observer set, and a firm-dominated signal); in that limit Spectral Brand Theory reduces to the incumbent, which is why the incumbent worked.", "papers": { "owns": [ "2026au" ], "imports": [], "refines": [] }, "relations": [ { "type": "contrasts", "target": "spectral-brand-theory" } ] }, { "key": "brand-metrology", "label": "Brand metrology", "owner": "2026au", "definition": "The stance that Spectral Brand Theory is an observational and measurement science of what a brand is and how it is read — the astronomer — rather than a brand-management practice — the astronaut; it supplies the experiment (the perception measurement) that a manager's decisions consume, and Blackwell's theorem is the bridge by which a finer measurement provably improves every decision without the measurement being a theory of any decision.", "papers": { "owns": [ "2026au" ], "imports": [ "2026av", "2026aw", "2026ax" ], "refines": [ "2026ax" ] }, "relations": [] }, { "key": "brand-perception-sde", "label": "Brand Perception SDE", "owner": "2026j", "definition": "A Stratonovich stochastic differential equation governing an observer's perception trajectory on the positive octant of the 7-sphere, with signal-encounter diffusion, signal-decay drift, and absorbing Dirichlet boundaries representing irreversible loss of a perceptual dimension.", "papers": { "owns": [ "2026j" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "brand-phase-space", "label": "Brand Phase Space", "owner": "2026z", "definition": "The 16-dimensional space $P=\\mathbb{R}^8 \\times \\mathbb{R}^8$ in which each brand occupies a point $(x(t),v(t))$ combining its spectral profile (position) and velocity, yielding a complete dynamic state description.", "papers": { "owns": [ "2026z" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "brand-signal-space", "label": "Brand Signal Space", "owner": "2026d", "definition": "The positive orthant of $\\mathbb{R}^8$ equipped with the Aitchison metric, representing brand emission profiles with multiplicative, compositional structure justified by Weber-Fechner scaling.", "papers": { "owns": [ "2026d" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "brand-spectrometer", "label": "Brand Spectrometer", "owner": "2026ax", "definition": "An applied measurement instrument that reconstructs cohort-resolved eight-dimensional brand-perception spec vectors from public artifacts through a fixed open pipeline (acquire -> render -> extract -> aggregate -> sensitivity) operated by cross-family LLM pairs. It is the applied apparatus built on the PRISM structured-measurement scaffold; its differentiator is not the renderer but the resolution it attaches via self-computed noise floors.", "papers": { "owns": [ "2026ax" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "brand-metrology" } ] }, { "key": "brand-triangulation", "label": "Brand Triangulation", "owner": "2026y", "definition": "A geometric framework that maps observer cohorts to GPS satellites, brand emission profiles to receiver location, and cohort biases to clock error, reframing inter-cohort perceptual disagreement as the geometric information from which a brand's eight-dimensional position is triangulated via weighted least squares.", "papers": { "owns": [ "2026y" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "brand-velocity", "label": "Brand Velocity", "owner": "2026z", "definition": "The first time derivative of a brand's spectral profile, $v(t)=dx/dt$, a vector in $\\mathbb{R}^8$ encoding the rate and direction of perceptual change across dimensions.", "papers": { "owns": [ "2026z" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "broadcast-a-dimension", "label": "Broadcast a dimension", "owner": "2026av", "definition": "The address-free activation bridge: emit a brand signal strong on the perceptual dimension a target cohort is sensitive to and let self-selection route it, so observers whose spectral-sensitivity profile peaks on that dimension perceive a salient signal (resonate) while off-peak observers receive a metamer-to-null. Formally a separating signal on a degraded broadcast channel whose per-observer channel quality is the projection of the signal onto the observer's sensitivity vector; the cohort is selected, not addressed.", "papers": { "owns": [ "2026av" ], "imports": [], "refines": [] }, "relations": [ { "type": "contrasts", "target": "perception-to-proxy-join" } ] }, { "key": "bundle-as-render", "label": "Bundle as render", "owner": "2026u", "definition": "The view that a paper's published bundle (the prose plus its claim graph, ontology module, and rendered glossary) is a render of the substrate at a point on its timeline, kept consistent with the source by the anti-drift gate.", "papers": { "owns": [ "2026u" ], "imports": [], "refines": [] }, "relations": [ { "type": "contrasts", "target": "substrate-as-repository" } ] }, { "key": "canon-as-repository", "label": "Canon as Repository", "owner": "2026w", "definition": "A specification-driven architecture that reconceives a transmedia franchise's canonical specification as a version-controlled repository in which editions are tagged commits, translations and adaptations are forks, canon governance operates through pull requests, and consistency validation functions as continuous integration.", "papers": { "owns": [ "2026w" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "capability-as-projection", "label": "Capability as projection", "owner": "2026al", "definition": "The claim that organizational capability is not a stored stock but a render-time projection computed from a query over the firm's cumulative event log.", "papers": { "owns": [ "2026al" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "cascade-consistency-condition", "label": "Cascade Consistency Condition", "owner": "2026ae", "definition": "The requirement that range($P_k$) is not contained in kernel($P_{k+1}$) for all $k$, ensuring each cascade level contributes independent information so the cascade remains full-rank.", "papers": { "owns": [ "2026ae" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "cascade-equilibrium", "label": "Cascade Equilibrium", "owner": "2026m", "definition": "The joint condition that each tier's projection is mutually consistent with the feedback of the tier below; it exists and is unique under tier-by-tier Banach contraction conditions.", "papers": { "owns": [ "2026m" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "cascade-position-prioritization", "label": "Cascade-Position Prioritization", "owner": "orgschema-audit", "definition": "The remediation principle (Proposition 1) that specification failures at higher cascade levels predict greater operational dysfunction than lower-level failures because higher-level failures invalidate the justification for all dependent levels.", "papers": { "owns": [ "2026ar" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "choice-operator-floor", "label": "Choice operator floor", "owner": "2026bb", "definition": "The noise floor of a choice elicitation: the mean pairwise disagreement rate between cross-family chooser models presented with identical (scenario, arrangement) trials. A divergence between revealed and predicted picks counts as a measured gap only when it exceeds k times this floor - so the gap is measured against choice noise, never asserted.", "papers": { "owns": [ "2026bb" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "operator-noise-floor" } ] }, { "key": "choice-perception-gap", "label": "Choice-perception gap", "owner": "2026bb", "definition": "The part of an AI observer's revealed brand choice that its stated eight-dimension perception does not predict: the rate at which the model's actual pick in a simulated choice task diverges, beyond the choice operator floor, from the cosine-nearest brand to the elicited need vector under the stated readings. It measures the wedge between perception-level and choice-level measurement as agentic systems move from describing brands to choosing them.", "papers": { "owns": [ "2026bb" ], "imports": [], "refines": [] }, "relations": [ { "type": "contrasts", "target": "perception-dop" } ] }, { "key": "classical-brand-regime", "label": "Classical brand regime", "owner": "2026au", "definition": "The corner of brand conditions in which all four regime-departure parameters are at their minimum — a tight unimodal perception cloud, slow dynamics, human-only observers, and a firm-dominated signal — and in which the cheap aggregate brand-health score is a sufficient statistic for managerial decisions, so the incumbent framework is the correct and cheaper tool.", "papers": { "owns": [ "2026au" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "cloud-valence", "label": "cloud valence", "owner": "2026a", "definition": "The valence of a perception cloud: positive, negative, or ambivalent. SBT does not use \"neutral\" for cloud valence; an undecided cloud is ambivalent.", "papers": { "owns": [ "2026a" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "coherence-floor", "label": "Coherence floor", "owner": "substrate-floor", "definition": "The noise floor of a specification-based instrument: specification incoherence $1-\\mathrm{SCI}$ (one minus the Specification Coherence Index) plus an audit-coverage gap. A specification instrument abstains below its coherence floor; below it, the coverage-impossibility theorem makes the abstention mandated, not conventional.", "papers": { "owns": [ "2026ay" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "coherence-type", "label": "Coherence Type", "owner": "2026s", "definition": "A structural classification of brands by the geometric pattern of emission across the eight dimensions, comprising five types whose ordering predicts crisis resilience better than a scalar coherence score.", "papers": { "owns": [ "2026s" ], "imports": [ "2026az", "2026ba", "2026bb" ], "refines": [] }, "relations": [] }, { "key": "cohort", "label": "cohort", "owner": "2026a", "definition": "A perceptual grouping of observers with similar spectral profiles, with dynamic membership. Cohorts are perceptual; demographics are metadata, not mechanism. Also written \"observer cohort\".", "papers": { "owns": [ "2026a" ], "imports": [ "2026aa", "2026ac", "2026ad", "2026af", "2026ah", "2026ar", "2026as", "2026at", "2026au", "2026av", "2026aw", "2026ax", "2026ay", "2026az", "2026b", "2026bb", "2026bc", "2026c", "2026d", "2026e", "2026f", "2026g", "2026j", "2026k", "2026n", "2026o", "2026p", "2026r", "2026v", "2026y", "2026z" ], "refines": [] }, "relations": [] }, { "key": "cohort-separability", "label": "Cohort Separability", "owner": "2026ad", "definition": "The property that cohort perception clouds remain distinct almost-invariant sets, governed by a strictly positive spectral gap of the perception operator.", "papers": { "owns": [ "2026ad" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "commit-reveal-priority", "label": "Commit-reveal privacy primitive", "owner": "2026u", "definition": "A primitive that lets researchers establish cryptographic priority and provenance through public commit hashes while keeping content disclosure under their own control.", "papers": { "owns": [ "2026u" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "compound-gap", "label": "Compound Gap", "owner": "2026c", "definition": "The simultaneous absence, across ten intellectual traditions, of high-dimensional geometric structure, a generative signal mechanism, observer heterogeneity, and non-ergodic temporal dynamics in any single integrated theory of brand perception.", "papers": { "owns": [ "2026c" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "concentration-premium", "label": "Concentration Premium", "owner": "2026k", "definition": "The result that cohorts with more concentrated weight profiles (higher Herfindahl index) yield strictly higher optimal perceived value, making niche cohorts inherently more valuable to serve than diffuse mass-market cohorts at equal cost.", "papers": { "owns": [ "2026k" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "conflict-class", "label": "CONFLICT", "owner": "federated-negotiation", "definition": "The interaction class where both authors own the same term_key with different def_hash; UNRESOLVED (fails the gate); SKOS closeMatch (same concept, divergent definition) or relatedMatch (key collides on distinct concepts); reconciliation operation NAMESPACE the colliding keys + curate the mapping, FORK the loser's key if the concepts truly differ.", "papers": { "owns": [ "2026at" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "interaction-class" } ] }, { "key": "content-addressed-module", "label": "Content-addressed vocabulary module", "owner": "federated-negotiation", "definition": "A small content-addressed triple (owner, term-set, import/refine relations) in which each owned term carries a definition whose sha256 (the def_hash) is the term's identity, so a changed definition is automatically a new identity with no human identifier-minting.", "papers": { "owns": [ "2026at" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "corrective-coherence-emission-rate", "label": "Corrective Coherence Emission Rate", "owner": "2026ad", "definition": "The rate at which purposive brand emissions inject observer mass back into the dominant cohort eigenspace per unit time.", "papers": { "owns": [ "2026ad" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "counter-cultural-decay", "label": "Counter-Cultural Decay", "owner": "2026p", "definition": "The temporal erosion of a signal's ideological distinctiveness as the cultural background field shifts and once counter-cultural positioning becomes normative.", "papers": { "owns": [ "2026p" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "coverage-impossibility", "label": "Coverage Impossibility", "owner": "2026h", "definition": "The geometric result that any finite collection of organizational specifications covers a negligible fraction of the 48-dimensional specification space, making exhaustive specification geometrically impossible regardless of cognitive capacity.", "papers": { "owns": [ "2026h" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "cross-import-class", "label": "CROSS_IMPORT", "owner": "federated-negotiation", "definition": "The interaction class where one author imports a term the other author owns; resolved; a clean cross-author dependency edge (SKOS exactMatch); no reconciliation operation needed.", "papers": { "owns": [ "2026at" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "interaction-class" } ] }, { "key": "cross-refine-class", "label": "CROSS_REFINE", "owner": "federated-negotiation", "definition": "The interaction class where one author refines a term the other owns with an explicit narrows_to; resolved; SKOS narrowMatch; reconciliation operation REBASE (the refiner's term becomes a narrows edge onto the owner's term).", "papers": { "owns": [ "2026at" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "interaction-class" } ] }, { "key": "cross-substrate-dispersion", "label": "Cross-substrate dispersion", "owner": "substrate-floor", "definition": "The maximum pairwise distance over the resolving instruments' verdict values on a common normalized axis in $[0,1]$ (the operator-floor move, lifted across instruments). It is the quantity read as the substrate floor and over which the reconciliation lattice is computed.", "papers": { "owns": [ "2026ay" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "d-a-ratio", "label": "D/A ratio", "owner": "2026a", "definition": "The designed/ambient ratio: the proportion of a brand's received signal that is intentionally designed versus ambient. Goldilocks zone 55-65% designed.", "papers": { "owns": [ "2026a" ], "imports": [ "2026j" ], "refines": [] }, "relations": [] }, { "key": "dangling-import-class", "label": "DANGLING_IMPORT", "owner": "federated-negotiation", "definition": "The interaction class where one author imports or refines a term that NEITHER author owns; UNRESOLVED (fails the gate); reconciliation operation BLOCK until some author introduces and owns the term or the import is dropped.", "papers": { "owns": [ "2026at" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "interaction-class" } ] }, { "key": "def-hash-identity", "label": "Definition-hash identity", "owner": "federated-negotiation", "definition": "The content-addressed identity of a term: the sha256 of its trimmed definition text (truncated to 16 hex). Two terms are the same iff their def_hash is byte-identical; a substantive definitional change yields a new identity automatically — the byte-exact strengthening of the OBO Foundry 'changed definition warrants a new identifier' policy.", "papers": { "owns": [ "2026at" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "differential-brand-measurement", "label": "Differential brand measurement", "owner": "2026y", "definition": "A calibration protocol, analogous to Differential GPS, that uses reference brands with known spectral profiles to correct systematic observer bias and separate brand-position change from observer drift in longitudinal studies.", "papers": { "owns": [ "2026y" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "dimensional-choice-weights", "label": "Dimensional choice weights", "owner": "2026bb", "definition": "The conditional-logit coefficients mapping per-dimension stated distances between brand and need onto revealed choice: the estimable answer to which of the eight dimensions agentic choice actually weights, including sign reversals where greater stated distance predicts being chosen. The choice-side analogue of the perception-side dimensional-collapse measurement.", "papers": { "owns": [ "2026bb" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "dimensional-collapse", "label": "Dimensional Collapse", "owner": "2026v", "definition": "The systematic compression by LLMs of an eight-dimensional brand emission profile toward a low-rank (chiefly Experiential and Economic) silhouette, rendering brands differentiated on other dimensions functionally equivalent in AI recommendations.", "papers": { "owns": [ "2026v" ], "imports": [ "2026au", "2026av" ], "refines": [] }, "relations": [] }, { "key": "dimensional-collapse-index", "label": "Dimensional Collapse Index", "owner": "2026v", "definition": "A scalar summary statistic (uniform baseline = .250) quantifying how severely an LLM concentrates implicit spectral weight onto verifiable dimensions, measuring the extent of dimensional collapse.", "papers": { "owns": [ "2026v" ], "imports": [ "2026as", "2026az" ], "refines": [] }, "relations": [] }, { "key": "dimensional-creation", "label": "Dimensional Creation", "owner": "2026p", "definition": "The activation of a previously null perceptual dimension that opens new uncrowded perceptual territory rather than competing within existing dimensional space.", "papers": { "owns": [ "2026p" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "directed-gradient-dominance", "label": "Directed-gradient dominance", "owner": "2026au", "definition": "The decision-efficiency result that outside the classical regime the full perception measurement weakly Blackwell-dominates the aggregate score for every decision-maker, so the cloud-optimizing manager moves the signal only along dimension-and-cohort directions whose payoff is observable, while the score-optimizing manager allocates effort along unobserved directions whose sign it cannot determine.", "papers": { "owns": [ "2026au" ], "imports": [], "refines": [] }, "relations": [ { "type": "contrasts", "target": "blind-spend" } ] }, { "key": "directional-coherence", "label": "Directional Coherence", "owner": "2026z", "definition": "The cosine similarity between a brand's velocity vector and an a priori strategy direction vector, quantifying alignment between actual brand movement and strategic intent.", "papers": { "owns": [ "2026z" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "distinctiveness-persistence-ordering", "label": "Distinctiveness-persistence ordering", "owner": "2026aw", "definition": "The result that a brand's perception-decay time constant tau is increasing in its off-generic distinctiveness sin-squared-beta (d tau / d sin-squared-beta > 0): a more distinctive brand sits at a deeper, better-separated stable point whose basin resists relaxation toward the generic centroid, so its formed perception persists longer. The same sin-squared-beta that is a perception-metamerism loss (2026au) and the self-selection sharpness (2026av) is here the persistence driver, unifying reach and formation under one quantity.", "papers": { "owns": [ "2026aw" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "self-selection-filter" }, { "type": "specializes", "target": "spectral-metamerism" } ] }, { "key": "distributional-separation-metric", "label": "Distribution-level separation metric", "owner": "2026ax", "definition": "A discriminant metric that measures whole cohort CLOUDS rather than centroids: energy distance and kernel maximum-mean-discrepancy (RBF, median-heuristic) between source-level cohort samples under a shared permutation null, plus an operator-floored distributional signal-to-noise (pair energy distance / max endpoint distributional operator floor) with a source-cluster bootstrap, and a magnitude/shape decomposition. It retains the MAGNITUDE the scale-invariant mean-cosine metric discards, so it is the magnitude-sensitive companion to the per-pair (cosine) resolution criterion.", "papers": { "owns": [ "2026ax" ], "imports": [], "refines": [] }, "relations": [ { "type": "contrasts", "target": "per-pair-resolution-criterion" }, { "type": "specializes", "target": "spectral-metamerism" } ] }, { "key": "drift-isotropy", "label": "Drift Isotropy", "owner": "2026s", "definition": "A characterization of a brand's signal-driven drift field by whether all dimensions clear an absolute drift floor (isotropic/robust) versus concentrate drift on k active dimensions leaving passive vulnerability corridors (k-anisotropic).", "papers": { "owns": [ "2026s" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "ecosystem-coherence", "label": "Ecosystem Coherence", "owner": "2026s", "definition": "A coherence type in which all eight dimensions emit and reinforce one another (isotropic drift), yielding the highest crisis resilience; exemplar Hermes.", "papers": { "owns": [ "2026s" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "effective-dimensionality-reduction", "label": "Effective Dimensionality Reduction", "owner": "2026h", "definition": "The reduction of the 48-dimensional specification space to $d_{\\text{eff}} = 8(1-(1-\\gamma)^6)/\\gamma$ free dimensions under OST cascade coupling strength $\\gamma$, yielding 15.75 dimensions at $\\gamma=0.5$.", "papers": { "owns": [ "2026h" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "epistemic-separation", "label": "Epistemic Separation", "owner": "2026b", "definition": "The architectural principle that observations, hypotheses, and knowledge (atoms, clouds, facts) are stored and processed as structurally distinct stages with no shortcut promotion or demotion between them.", "papers": { "owns": [ "2026b" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "ergodicity-coefficient", "label": "ergodicity coefficient", "owner": "2026o", "definition": "A per-dimension metric (epsilon) quantifying how far an observer cohort's perception departs from ergodicity. A reliability-of-aggregation measure, not a generic reliability score.", "papers": { "owns": [ "2026o" ], "imports": [ "2026j" ], "refines": [] }, "relations": [] }, { "key": "experiential-asymmetry", "label": "Experiential Asymmetry", "owner": "2026s", "definition": "A coherence type with emission concentrated on the experiential and social dimensions, producing divergent direct-encounter versus mediated perceptions; exemplar Erewhon.", "papers": { "owns": [ "2026s" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "federated-ci-gate", "label": "Federated CI gate", "owner": "federated-negotiation", "definition": "The continuous-integration semantics of the federated linker: --gate exits nonzero (fails the build) iff any cross-owner interaction is in one of the three unresolved classes (CONFLICT, INCOMPATIBLE_REFINE, DANGLING_IMPORT); a passing gate certifies a linkable federation.", "papers": { "owns": [ "2026at" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "federated-ontology-negotiation", "label": "Federated ontology negotiation", "owner": "federated-negotiation", "definition": "The cross-author generalization of single-author ontology linking: given two namespaced module sets from distinct authorities, mechanically classify every cross-owner term interaction and propose a typed, justified reconciliation, before either author reads the other's prose.", "papers": { "owns": [ "2026at" ], "imports": [ "2026ay" ], "refines": [] }, "relations": [ { "type": "narrows", "target": "link-time-compatibility-check" } ] }, { "key": "floor-nesting", "label": "Floor nesting", "owner": "substrate-floor", "definition": "The partial order on noise floors, operator $\\subseteq$ artifact $\\subseteq$ substrate: a finding survives only if its signal clears the OUTERMOST floor in play, $\\mathrm{effective\\_floor}=\\max(\\mathrm{substrate\\_dispersion},\\, f_1,\\dots,f_n)$ over each endpoint's own combined floor $f_i$. The same criterion composes within one instrument and across instruments.", "papers": { "owns": [ "2026ay" ], "imports": [ "2026ba" ], "refines": [] }, "relations": [ { "type": "contrasts", "target": "substrate-floor" } ] }, { "key": "forced-perception-dynamics", "label": "Forced perception dynamics", "owner": "2026aw", "definition": "The model of brand-perception formation and maintenance as a forced Ornstein-Uhlenbeck system on the eight-dimensional SBT manifold: the perception cloud's centroid obeys dX = [-A(X - x*) + F(t)] dt + Sigma dW, where A is the restoring (relaxation) operator, x* the intrinsic stable point, and F(t) the campaign forcing vector. Formation is the forced transient toward a target displacement, maintenance is sustained forcing balancing the restoring force, and 'stop advertising -> perception decays' is the unforced relaxation toward x*. It subsumes the scalar advertising-stock-with-decay tradition (goodwill/response models) as the one-dimensional projection.", "papers": { "owns": [ "2026aw" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "brand-metrology" }, { "type": "specializes", "target": "spectral-dynamics" } ] }, { "key": "forcing-function", "label": "Forcing function (campaign)", "owner": "2026aw", "definition": "A marketing campaign represented as a time-varying vector F(t) in the same spectral basis as the perception cloud, entering the drift of the forced-perception-dynamics SDE. Each marketing action (advertising, launch, pricing, endorsement) contributes a force on the cloud; the net force is their vector sum. Formation and maintenance differ only in F(t)'s schedule relative to the relaxation rate.", "papers": { "owns": [ "2026aw" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "forkability-decomposition", "label": "Forkability as Subspace Decomposition", "owner": "2026h", "definition": "The geometric decomposition of the 48-dimensional specification space into a shared subspace and a private subspace, formalizing how organizations share higher-level specifications while diverging on lower levels.", "papers": { "owns": [ "2026h" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "full-rank-cascade", "label": "Full-Rank Cascade", "owner": "2026ae", "definition": "The OST acceptance-testing cascade modeled as a full-rank projection in which each hierarchical level independently projects onto a distinct performance subspace while preserving the specification's dimensional structure.", "papers": { "owns": [ "2026ae" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "function-as-friction-tax", "label": "Function-as-Friction-Tax", "owner": "2026am", "definition": "The proposition that interface-maintaining functional headcount and spend are a structural tax that scales with specification gaps rather than a discretionary governance choice.", "papers": { "owns": [ "2026am" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "garbling-severity-ladder", "label": "Garbling-severity ladder", "owner": "2026az", "definition": "The pre-registered ordering of aggregators by how much resolvable structure they destroy: the metameric fraction is predicted monotone in aggregator coarseness - fraction(scalar score) > fraction(ranking) > fraction(full readout) = 0 by construction. Making garbling severity an ordered, testable property is what upgrades the garbling account from interpretation to measurement.", "papers": { "owns": [ "2026az" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "identity-coherence", "label": "Identity Coherence", "owner": "2026s", "definition": "A coherence type with emission concentrated on the ideological and narrative dimensions, highly resilient except to ideological betrayal; exemplar Patagonia.", "papers": { "owns": [ "2026s" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "identity-gate", "label": "Identity Gate", "owner": "2026b", "definition": "A binary precondition requiring a core-identity match before any multi-dimensional comparison or clustering of atoms is attempted.", "papers": { "owns": [ "2026b" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "incoherent-coherence", "label": "Incoherent", "owner": "2026s", "definition": "A coherence type marked by extreme cross-dimensional variance and contradictory signals yielding a stochastic drift field and lowest resilience; exemplar Tesla.", "papers": { "owns": [ "2026s" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "incompatible-refine-class", "label": "INCOMPATIBLE_REFINE", "owner": "federated-negotiation", "definition": "The interaction class where one author refines a term the other owns WITHOUT a narrows_to; UNRESOLVED (fails the gate); reconciliation operation BLOCK until the refiner supplies an explicit narrowing. The well-formed-module discipline (refine requires narrows_to) forecloses this class on disciplined inputs.", "papers": { "owns": [ "2026at" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "interaction-class" } ] }, { "key": "incumbent-garbling-operator", "label": "Incumbent garbling operator", "owner": "2026au", "definition": "The measurable projection-and-aggregation map T_k = A_k composed with Pi_k that represents an incumbent brand-equity framework as a low-order summary of the perception cloud; observing T_k(mu) is a Blackwell garbling of observing the full perception measurement mu, so by the data-processing inequality it is weakly less informative for every decision problem (the representation lemma).", "papers": { "owns": [ "2026au" ], "imports": [ "2026av", "2026az" ], "refines": [] }, "relations": [] }, { "key": "interaction-class", "label": "Cross-owner interaction class", "owner": "federated-negotiation", "definition": "One of exactly six mutually-exclusive, exhaustive classes that a total classification function assigns to every cross-owner term interaction between two authors' module sets; each class carries a SKOS predicate, a reconciliation operation, and federated-CI gate semantics.", "papers": { "owns": [ "2026at" ], "imports": [], "refines": [] }, "relations": [ { "type": "contrasts", "target": "federated-ci-gate" } ] }, { "key": "levels-of-reading", "label": "Levels of Reading", "owner": "foam-bridge-note", "definition": "A four-level model of reading depth induced by the producer-observer pipeline read observer-side: an observer of the same rendered artifact may stop at their own perception, reach the meaningfulness (the rendered work as an object), reach the meaning (the recoverable specification), or reach toward the substrate (the upstream intent); ascending the levels is progressively decentering away from the observer's own projection toward the work itself.", "papers": { "owns": [ "2026bc" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "link-time-compatibility-check", "label": "Link-time compatibility check", "owner": "2026u", "definition": "A check, performed by a linker over the corpus's per-paper modules, that treats each paper as a module in a typed codebase and enforces one owner per term, no dangling import or refine, compatible refinement, and acyclic narrowing — the type-checking step of the substrate-as-repository.", "papers": { "owns": [ "2026u" ], "imports": [], "refines": [ "2026at" ] }, "relations": [] }, { "key": "live-panel", "label": "Live panel", "owner": "2026ba", "definition": "The companion panel of fresh artifacts re-collected for the same brands at each version epoch. Its inter-epoch movement carries apparatus drift PLUS brand signal; subtracting the pinned version floor estimates the brand signal. At the birth epoch the live panel coincides with the pinned capture by construction.", "papers": { "owns": [ "2026ba" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "log-compatibility-function", "label": "Log-compatibility function", "owner": "2026al", "definition": "A function scoring how compatible two organizational logs are by counting event pairs that cannot be merged without violating determinism, predicting M&A transfer success.", "papers": { "owns": [ "2026al" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "maintenance-forcing-budget", "label": "Maintenance forcing budget", "owner": "2026aw", "definition": "The steady-state forcing F_hold = A d required to HOLD the perception cloud at a target displacement d from the brand's intrinsic stable point: the forcing that exactly cancels the restoring force. The maintenance budget equals the relaxation loss at the held displacement and falls to zero as the target approaches the brand's own stable point, so a distinctive brand holds its perception with little forcing and an undifferentiated one pays continuous forcing or collapses.", "papers": { "owns": [ "2026aw" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "meaning-channel", "label": "Meaning Channel", "owner": "2026r", "definition": "A pathway, rooted in a distinct academic tradition, through which a brand's emissions are interpreted by an observer to form a component of perception; the unit by which SBT dimensions are counted (bandwidth of transmission), as distinct from perceptual factors.", "papers": { "owns": [ "2026r" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "meaning-channel-vs-content-domain", "label": "Meaning-Channel versus Content-Domain Distinction", "owner": "2026r", "definition": "A principled stopping rule that separates genuine meaning-transmission channels (which count as dimensions) from content domains (processed through existing channels), preventing indefinite dimensional inflation.", "papers": { "owns": [ "2026r" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "meaning-vs-meaningfulness", "label": "Meaning vs Meaningfulness (structural)", "owner": "2026ao", "definition": "A structural distinction in which meaning is a property of the typed-graph substrate (transferable across renderings) and meaningfulness is a property of a specific cohort-conditional rendering.", "papers": { "owns": [ "2026ao" ], "imports": [ "2026ap" ], "refines": [] }, "relations": [] }, { "key": "measurement-to-activation-handoff-contract", "label": "Measurement-to-activation handoff contract", "owner": "2026av", "definition": "The specification that, for a target dimension and cohort, returns the recommended bridge mechanism from perception space to delivery and its quantified cost — the argmin over the three bridges of (targeting loss + delivery cost): a dimension-distinct cohort routes to broadcast-a-dimension at a cost equal to predicted spill, a reflection-surface-clustered cohort routes to provenance-as-address at a cost equal to coverage bias, else the minimal-loss proxy at a cost equal to the proxy-join loss. It keeps the brand-metrology division of labor: the instrument supplies the target and the bridge cost; the manager runs the media buy.", "papers": { "owns": [ "2026av" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "brand-metrology" } ] }, { "key": "metamer-pair", "label": "Metamer pair", "owner": "2026az", "definition": "The unit of measurement of PRISM-M: two brands whose full eight-dimension perception profiles are resolved distinct (pairwise distance exceeds k times the operator floor, pre-registered k = 2) while an aggregating readout leaves them unresolved (within the aggregator's own floor). Labelled MP- in the frozen pair bank; both halves of the criterion are measured against noise floors, never asserted.", "papers": { "owns": [ "2026az" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "spectral-metamerism" } ] }, { "key": "metameric-arbitrage", "label": "Metameric arbitrage", "owner": "2026au", "definition": "The pair of levers that metamerism opens and the aggregate model cannot see: signal-metamerism (distinct signals inducing equal perception) yields a cheaper-signal substitution within a perceptual equivalence class, and perception-metamerism (one signal inducing divergent perception across cohorts) yields a mis-targeting loss; the realized decision loss is bounded below by a quantity monotone in the four regime-departure parameters.", "papers": { "owns": [ "2026au" ], "imports": [ "2026av" ], "refines": [ "2026av" ] }, "relations": [ { "type": "specializes", "target": "spectral-metamerism" } ] }, { "key": "metameric-degree", "label": "Metameric degree", "owner": "2026ax", "definition": "The composite scalar 1 - mean cosine similarity across all cohort pairs of an atlas; a low value means the cohort CENTROIDS bunch in dimensional shape. On the atom-averaged fresh window it is .0158 (matching the cohort-attributable variance in the V2 decomposition) and .0079 on the pinned window. A low metameric degree is shape-convergence only; it does not preclude a magnitude separation that the distribution-level metric resolves.", "papers": { "owns": [ "2026ax" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "spectral-metamerism" } ] }, { "key": "metameric-fraction", "label": "Metameric fraction", "owner": "2026az", "definition": "The share of resolvable brand distinctions that an aggregating readout destroys: the proportion of brand pairs resolved as distinct on the full eight-dimension readout (distance clears the operator floor) that the aggregator renders unresolved (within the aggregator's own floor). It operationalizes spectral metamerism as a measured quantity with an operator-floored bootstrap interval, monotone in the garbling severity of the aggregator.", "papers": { "owns": [ "2026az" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "spectral-metamerism" } ] }, { "key": "metameric-observer", "label": "Metameric observer (LLM)", "owner": "2026v", "definition": "The characterization of LLMs as observers that produce convergent brand recommendations from structurally divergent brand inputs because their spectral weights collapse the differentiating dimensions to near-zero.", "papers": { "owns": [ "2026v" ], "imports": [ "2026au", "2026av", "2026az", "2026bb", "2026x" ], "refines": [] }, "relations": [] }, { "key": "metameric-psychometrics", "label": "Metameric psychometrics", "owner": "2026ax", "definition": "A validation class for ground-truth-absent perception measurement: reliability, convergent validity, reproducibility, and discriminant resolution are established against noise floors the instrument computes for itself, never against a latent true score or a human-panel oracle. Cohort metameric variance is treated as the measurement, not as error; 'is this difference real?' becomes the quantified, falsifiable question of whether a cohort distance exceeds the instrument's own operator and artifact floors. Reliability/convergent/reproducibility hold unconditionally; discriminant resolution is conditional on cohort signal exceeding noise.", "papers": { "owns": [ "2026ax" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "spectral-metamerism" } ] }, { "key": "metamerism-set", "label": "Metamerism Set", "owner": "org-as-metadata", "definition": "The collection of configurations that map to identical value outputs for a given observer and process, a derived quantity that expands as coordination costs fall and contracts as tacit knowledge intensity rises.", "papers": { "owns": [ "2026af" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "multi-brand-capacity-diagnostic", "label": "Multi-Brand Capacity Diagnostic (MBCD)", "owner": "2026ah", "definition": "A diagnostic instrument that extends the Six-Tier Separability Diagnostic to predict how many additional brands a firm can host on its current brand-agnostic substrate without performance degradation.", "papers": { "owns": [ "2026ah" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "multi-interface-specification-model", "label": "Multi-Interface Specification Model", "owner": "2026am", "definition": "A three-layer decomposition of organizational output architecture into a codified specification substrate, an interface layer of recipient-class renderings, and a function layer that maintains spec-to-interface alignment.", "papers": { "owns": [ "2026am" ], "imports": [ "2026an" ], "refines": [] }, "relations": [] }, { "key": "need-vector", "label": "Need vector", "owner": "2026bb", "definition": "A buyer need expressed in the same eight-dimension space as brand readings: the scenario's stated need is rendered as ideal-brand prose and extracted with the unchanged PRISM-B extractor, so need and brand live in one space and the cosine-nearest brand is a well-defined predicted pick.", "papers": { "owns": [ "2026bb" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "non-ergodic-perception", "label": "non-ergodic perception", "owner": "2026o", "definition": "The property that the time-average of a single observer's brand perception does not equal the ensemble-average across the cohort, so cross-sectional brand measures cannot be substituted for longitudinal ones. A distinct concept from non-stationarity; cite Peters (2019) when using the framing.", "papers": { "owns": [ "2026o" ], "imports": [ "2026ad", "2026au", "2026c", "2026d", "2026f", "2026j", "2026m", "2026s", "2026z" ], "refines": [] }, "relations": [] }, { "key": "observer-depth", "label": "Observer Depth", "owner": "foam-bridge-note", "definition": "The deepest level of reading an observer's extraction currently reaches, operationalizable as coverage of the source specification recovered by the observer's extraction; it increases with observer maturation, and a meaning-depth reading is exactly the reading positioned to check rendering equivalence.", "papers": { "owns": [ "2026bc" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "observer-driven-evolution-thesis", "label": "Observer-driven evolution thesis", "owner": "2026x", "definition": "A synthesizing framework holding that brand-identity verification technologies change discontinuously, not incrementally, in response to a change in the primary observer type (wax seals, hallmarks, trademarks, SSL certificates, and now AI agents).", "papers": { "owns": [ "2026x" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "observer-spectral-profile", "label": "observer spectral profile", "owner": "2026a", "definition": "The receiver-side object that collapses a brand signal into a conviction. Five components: spectrum, weights, tolerances, priors, and an identity gate. Cohorts are observers, not consumers.", "papers": { "owns": [ "2026a" ], "imports": [ "2026aa", "2026ac", "2026af", "2026ah", "2026ai", "2026as", "2026au", "2026av", "2026aw", "2026ax", "2026b", "2026bc", "2026c", "2026d", "2026e", "2026f", "2026g", "2026j", "2026k", "2026n", "2026p", "2026r", "2026s", "2026v", "2026x", "2026y", "2026z" ], "refines": [] }, "relations": [] }, { "key": "observer-weight-space", "label": "Observer Weight Space", "owner": "2026d", "definition": "The probability simplex $\\Delta^7$ equipped with the Fisher-Rao metric (unique under Cencov's theorem), representing observers' relative salience weights across the eight dimensions.", "papers": { "owns": [ "2026d" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "operator-noise-floor", "label": "Operator-noise floor", "owner": "2026ax", "definition": "The instrument-computed reliability floor for a cohort: the maximum cosine distance between the cohort's primary spec vector and the vectors produced by cross-family alternative operator pairs reading the same artifacts. It quantifies how much of a measured cohort difference is attributable to operator (renderer/extractor) substitution rather than to the cohort, and it is the threshold V1 (test-retest) and V2 (cross-operator) are read against.", "papers": { "owns": [ "2026ax" ], "imports": [ "2026az", "2026ba", "2026bb" ], "refines": [] }, "relations": [ { "type": "specializes", "target": "spectral-metamerism" } ] }, { "key": "operator-role", "label": "Operator (role-level abstraction)", "owner": "2026ao", "definition": "A role-level abstraction above the human-versus-AI instance distinction whose intrinsic structural-substrate and judgment operations are performed by a human/AI projection composition that varies by era.", "papers": { "owns": [ "2026ao" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "organization-as-metadata", "label": "Organization as Metadata", "owner": "org-as-metadata", "definition": "The mechanism framing organizational form as revisable metadata that specifies how processes are instantiated and coordinated without containing the productive logic itself, so configuration can change without altering value or process.", "papers": { "owns": [ "2026af" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "organizational-layer", "label": "Organizational Layer", "owner": "org-as-metadata", "definition": "The layer consisting of configurations of agents, roles, authority relationships, resource allocations, and coordination procedures assembled to execute processes, the most volatile layer because it is contingent on coordination technology.", "papers": { "owns": [ "2026af" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "organizational-metamerism", "label": "Organizational Metamerism", "owner": "org-as-metadata", "definition": "An observer-relative condition in which two structurally distinct organizational configurations executing the same process map to identical value outputs for a specific evaluator.", "papers": { "owns": [ "2026af" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "orgschema-audit", "label": "OrgSchema Audit", "owner": "orgschema-audit", "definition": "A structured diagnostic protocol that evaluates organizational specification maturity across six cascading levels, asking whether every operational parameter traces backward to a customer-experience justification and every experience goal traces forward to a verifiable implementation.", "papers": { "owns": [ "2026ar" ], "imports": [ "2026ay" ], "refines": [] }, "relations": [] }, { "key": "peer-alignment-event", "label": "Peer alignment event", "owner": "2026u", "definition": "A reconception of journal publication not as the endpoint of research but as a synchronization point at which the scientific community confirms that a render of the ongoing research is sound at a given stage.", "papers": { "owns": [ "2026u" ], "imports": [ "2026at" ], "refines": [] }, "relations": [] }, { "key": "per-pair-resolution-criterion", "label": "Per-pair resolution criterion", "owner": "2026ax", "definition": "The decision rule by which a cohort pair is judged resolved, marginal, or sub-resolution: per-pair signal-to-noise S/N = cohort_pairwise_distance / max(endpoint cohorts' operator-noise floors), with resolved at S/N > 2, marginal at 1 <= S/N <= 2, and sub-resolution at S/N < 1. A pair below its floor cannot be distinguished from operator noise and is reported as sub-resolution, never as a finding.", "papers": { "owns": [ "2026ax" ], "imports": [ "2026az", "2026ba" ], "refines": [] }, "relations": [] }, { "key": "perception-cloud", "label": "perception cloud", "owner": "2026a", "definition": "The distribution of brand convictions across an observer population for a brand. Distributional, not a single fixed referent; \"cloud\" alone is acceptable in context. Has a valence (positive / negative / ambivalent).", "papers": { "owns": [ "2026a" ], "imports": [ "2026ac", "2026ad", "2026ah", "2026ai", "2026as", "2026at", "2026au", "2026av", "2026aw", "2026ax", "2026b", "2026bc", "2026c", "2026e", "2026j", "2026k", "2026n", "2026o", "2026p", "2026v", "2026w", "2026z" ], "refines": [] }, "relations": [] }, { "key": "perception-cloud-as-foam", "label": "Foam (Perception-Cloud Image)", "owner": "foam-bridge-note", "definition": "A one-time framing image for the perception cloud's granular structure: a foam of per-observer perception bubbles whose collective surface, seen from a distance, is the cohort's perception cloud. The canonical term is perception cloud; foam is an image used once on first introduction, never a load-carrying noun.", "papers": { "owns": [ "2026bc" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "perception-decay-time-constant", "label": "Perception-decay time constant", "owner": "2026aw", "definition": "The relaxation time tau = 1 / lambda_min(A) of a brand's perception cloud — the inverse of the slowest eigenvalue of the restoring operator — governing how fast the centroid displacement relaxes toward the intrinsic stable point once forcing stops (||x_bar(t) - x*|| ~ exp(-t/tau)). The SBT-native reading of advertising adstock/mental-availability decay; recoverable from a time-sliced reflection series spanning a spend pulse and its aftermath.", "papers": { "owns": [ "2026aw" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "perception-dop", "label": "Perception DOP", "owner": "2026y", "definition": "A scalar metric computed solely from proposed cohort weight profiles (before any data collection) that quantifies the expected precision with which a given observer-cohort configuration can resolve a brand's eight-dimensional spectral profile.", "papers": { "owns": [ "2026y" ], "imports": [ "2026as", "2026bb" ], "refines": [] }, "relations": [] }, { "key": "perception-to-proxy-join", "label": "Perception-to-proxy join", "owner": "2026av", "definition": "The activation bridge that maps a perceptual cohort onto addressable proxy features (platform, geography, register, recency, panel demographics) stored alongside the eight-dimensional vector. The map is a Blackwell garbling of the perceptual experiment, so it is weakly less valuable for the targeting decision; its cost is the proxy-join loss.", "papers": { "owns": [ "2026av" ], "imports": [], "refines": [] }, "relations": [ { "type": "specializes", "target": "incumbent-garbling-operator" } ] }, { "key": "perceptual-stable-point", "label": "Perceptual stable point", "owner": "2026aw", "definition": "The intrinsic equilibrium x* of a brand's perception cloud — the perception it relaxes toward when unforced — equivalently the bottom of the potential well of the drift field. A distinctive brand's stable point is deep and well-separated from the generic perceptual centroid; the long-run equilibrium of the brand-knowledge structure the static brand-equity tradition describes.", "papers": { "owns": [ "2026aw" ], "imports": [], "refines": [] }, "relations": [ { "type": "contrasts", "target": "re-collapse" } ] }, { "key": "perceptual-threshold", "label": "Perceptual Threshold", "owner": "2026g", "definition": "The Aitchison-distance parameter epsilon below which two brands are confusable and above which they are distinguishable, grounded in the psychophysical just-noticeable-difference concept and varying with observer expertise and context.", "papers": { "owns": [ "2026g" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "pinned-panel", "label": "Pinned panel", "owner": "2026ba", "definition": "An artifact panel captured once and stored byte-identical (hash-sealed), re-read at every model-version epoch. Since the input never changes, ALL movement on the pinned panel is apparatus drift - the identification guarantee of the pinned/live decomposition. The pinned panel is a calibration standard, not a representation of the current brand; its staleness is the point.", "papers": { "owns": [ "2026ba" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "portfolio-spectral-interference", "label": "Portfolio Spectral Interference", "owner": "2026p", "definition": "A mechanism whereby contradictory signals emitted on the same dimension by two brands sharing a parent company contaminate each other's perception once the observer becomes aware of the shared parentage.", "papers": { "owns": [ "2026p" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "position-triple", "label": "Position Triple", "owner": "2026m", "definition": "The formal decomposition of any position as p = (P_p, A_p, R_p), where perceptual content inherits from routines, authority inherits from governance, and role expectation inherits from cultural commitments.", "papers": { "owns": [ "2026m" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "positioning-capacity", "label": "Positioning Capacity", "owner": "2026g", "definition": "The maximum number of distinguishable (pairwise-distance exceeding the perceptual threshold) brand positions a market's brand space can sustain, bounded via sphere-packing arguments using the E8 lattice in eight dimensions.", "papers": { "owns": [ "2026g" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "prism-b", "label": "PRISM-B", "owner": "prism", "definition": "The brand-perception PRISM variant: eight scale items mapped one-to-one to SBT dimensions on a 1-5 ordinal format measuring perceived signal-reception intensity, with an exact prompt template and scoring algorithm.", "papers": { "owns": [ "2026as" ], "imports": [ "2026bb", "2026v" ], "refines": [] }, "relations": [] }, { "key": "prism-c", "label": "PRISM-C", "owner": "2026bb", "definition": "The choice member of the PRISM instrument family: an AI-observer instrument that measures a model's revealed choice among brands in a simulated agentic task and compares it to the model's stated eight-dimension perception (PRISM-B), quantifying the choice-perception gap and the dimensional weights that map stated perception to revealed choice.", "papers": { "owns": [ "2026bb" ], "imports": [ "2026ax" ], "refines": [] }, "relations": [] }, { "key": "prism-five-layer-scaffold", "label": "PRISM Five-Layer Scaffold", "owner": "prism", "definition": "The reusable PRISM protocol architecture separating specification (PL0), configuration (PL1), prompts (PL2), sessions (PL3), and analysis (PL4) so instrument variants share infrastructure while varying items.", "papers": { "owns": [ "2026as" ], "imports": [ "2026az", "2026ba", "2026bb" ], "refines": [] }, "relations": [] }, { "key": "prism-instrument", "label": "PRISM", "owner": "prism", "definition": "A family of standardized instruments for eliciting multi-dimensional brand perception from both AI and human observers within SBT, built on a domain-neutral five-layer scaffold.", "papers": { "owns": [ "2026as" ], "imports": [ "2026az", "2026ba", "2026bb" ], "refines": [] }, "relations": [] }, { "key": "prism-m", "label": "PRISM-M", "owner": "2026az", "definition": "The metamerism member of the PRISM instrument family: an AI-observer instrument that measures when two brands with structurally distinct eight-dimension perception profiles become perceptually indistinguishable under an aggregating readout (a scalar health score, a search ranking, a recommendation pick). Its unit is the metamer pair and its output is the metameric fraction.", "papers": { "owns": [ "2026az" ], "imports": [ "2026ax" ], "refines": [] }, "relations": [] }, { "key": "prism-t", "label": "PRISM-T", "owner": "2026ba", "definition": "The temporal member of the PRISM instrument family: an AI-observer instrument that separates apparatus drift (the same artifacts read differently by a new model version) from brand-signal change (the artifacts themselves changed) when a vendor ships a new model version. Its unit is the (brand, version-epoch) reading and its output is the version floor plus the pinned/live drift decomposition.", "papers": { "owns": [ "2026ba" ], "imports": [ "2026ax" ], "refines": [] }, "relations": [] }, { "key": "projection-cascade", "label": "Projection Cascade", "owner": "2026m", "definition": "A six-tier sequence of rank-reducing linear projection operators linking owner intent, business model, governance, architecture, routines, and positions, in which each junction carries a rank deficiency that bounds downstream information loss.", "papers": { "owns": [ "2026m" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "projection-operator", "label": "Projection operator", "owner": "2026al", "definition": "A function that reads a query-relevant subset of the log at a render time and produces an observable capability claim.", "papers": { "owns": [ "2026al" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "provenance-as-address", "label": "Provenance as address", "owner": "2026av", "definition": "The activation bridge that traces a perceptual cohort back to re-reachable channels using the source, platform, geography, and content-date provenance each Brand Spectrometer reflection already carries: a cohort of reflections is a recency-aware list of surfaces where the perception is currently expressed. A special case of the perception-to-proxy join in which the proxy features are natively addressable rather than statistically inferred; its cost is the coverage bias of the harvested surfaces (the silent majority may not surface).", "papers": { "owns": [ "2026av" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "proxy-join-loss", "label": "Proxy-join loss", "owner": "2026av", "definition": "The expected decision loss L(P) of targeting a perceptual cohort C through an addressable proxy P, non-negative and ordered by the informativeness of P about cohort membership (the mutual information between membership and the proxy); the minimal-loss proxy P-star maximizes that information. When L(P-star) exceeds the predicted spill of broadcast-a-dimension the handoff contract routes to broadcast, making the reach choice a measured comparison rather than a default to addressability.", "papers": { "owns": [ "2026av" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "rank-1-audit", "label": "Rank-1 Audit", "owner": "2026ae", "definition": "Conventional audit modeled as a degenerate rank-1 projection onto a single compliance axis, discarding by construction all information orthogonal to that axis.", "papers": { "owns": [ "2026ae" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "rasterized-vectorized-brand-management", "label": "Rasterized vs Vectorized Brand Management", "owner": "2026e", "definition": "The distinction between rasterized brand management (a human projecting the full brand specification through lossy cognitive bottlenecks) and vectorized brand management (treating the full 8-dimensional spectral profile as single source of truth with channel outputs as computed projections of known, bounded loss).", "papers": { "owns": [ "2026e" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "re-collapse", "label": "re-collapse", "owner": "2026a", "definition": "The structural mechanism by which a brand signal is re-emitted and re-collapsed into a changed perception cloud. Names the mechanism; \"rebranding\" is only the conventional surface label. Always hyphenated.", "papers": { "owns": [ "2026a" ], "imports": [ "2026ae", "2026ah", "2026au", "2026aw", "2026b", "2026d", "2026j" ], "refines": [] }, "relations": [] }, { "key": "recipient-class", "label": "Recipient Class", "owner": "2026am", "definition": "An architectural primitive comprising a set of agents sharing a common perception geometry, access pattern, and decision context, toward which a distinct interface is rendered.", "papers": { "owns": [ "2026am" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "reconciliation-lattice", "label": "Reconciliation lattice", "owner": "substrate-floor", "definition": "The typed-verdict calculus returned over the cross-substrate dispersion floor on a common normalized verdict axis: corroborated (>=2 resolve, agree within floors, consensus clears the effective floor), contested (>=2 resolve, disagree beyond floors), substrate-conditional (exactly 1 resolves above its floor), jointly-unresolved (all abstain, or agreement on a consensus below the effective floor). A typed verdict, never a forced point estimate.", "papers": { "owns": [ "2026ay" ], "imports": [], "refines": [] }, "relations": [ { "type": "contrasts", "target": "cross-substrate-dispersion" } ] }, { "key": "reconciliation-operation", "label": "Reconciliation operation", "owner": "federated-negotiation", "definition": "One of lock / fork / rebase / merge — the single-author spine operation vocabulary lifted to operate across distinct owners, proposed per interaction class as the typed action that would reconcile it (MERGE for AGREEMENT, REBASE for CROSS_REFINE, NAMESPACE+FORK for CONFLICT, BLOCK for the dangling/incompatible cases).", "papers": { "owns": [ "2026at" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "recovery-salvage-matrix", "label": "Recovery Salvage Matrix", "owner": "2026ah", "definition": "A pre-failure infrastructure-audit instrument that converts the six-tier decomposition into a forecast of which brand-agnostic substrate is preserved when a Tier-4 brand fails.", "papers": { "owns": [ "2026ah" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "reflection", "label": "Reflection (per-artifact spectral measurement)", "owner": "2026ax", "definition": "The unit of measurement in the Brand Spectrometer: the brand signal as reflected through a single public artifact and read by one operator pair, yielding one eight-dimensional spec vector bound to one source. It is the data-of-record the instrument aggregates reflection -> source -> cohort, recomputable into cohorts at any resolution. The optics-native name is deliberate: a spectrometer measures reflected signal, and perception is completed in the observer (the brand 'has no colour' until reflected and read). Distinct from the atom-cloud-fact 'atom' (2026b), a single (dimension, source) cell of raw observation; a reflection bundles all eight dimensions from one source and is operator-produced, so it is not a refinement of that atom and does not edit it.", "papers": { "owns": [ "2026ax" ], "imports": [ "2026ba" ], "refines": [] }, "relations": [ { "type": "contrasts", "target": "atom" } ] }, { "key": "regime-departure-parameter", "label": "Regime-departure parameter", "owner": "2026au", "definition": "One of four separately-estimable quantities whose joint smallness defines the classical brand regime and whose growth measures the distance from it: perceptual dispersion/multimodality (sigma), temporal velocity (v), AI-observer share (alpha), and exogenous-signal share (epsilon). The decision loss of score-based management is bounded below by a quantity monotone non-decreasing in each.", "papers": { "owns": [ "2026au" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "regime-test", "label": "Regime test", "owner": "2026au", "definition": "The first step of the theorem-entailed managerial procedure: estimate the four regime-departure parameters for a category to decide whether the cheap aggregate brand-health score is in fact sufficient (so Spectral Brand Theory is not over-prescribed where the incumbent suffices) or whether the category has left the classical regime far enough that cloud-based management weakly dominates net of measurement cost.", "papers": { "owns": [ "2026au" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "rendering-equivalence", "label": "Rendering-Equivalence under Spine-Preservation", "owner": "2026ao", "definition": "P4: two prose renderings of a locked substrate arrive at the same conclusions if and only if both preserve the spine's structural elements, under the sigma-faithfulness axiom.", "papers": { "owns": [ "2026ao" ], "imports": [ "2026ap" ], "refines": [] }, "relations": [] }, { "key": "research-as-repository", "label": "Research as Repository", "owner": "2026u", "definition": "A protocol that treats every research program as a version-controlled repository (the evolving SSOT) of which a paper is a render at a point on its timeline, a submission is a fork, peer review is attributed commits on a review branch, and publication is a merge.", "papers": { "owns": [ "2026u" ], "imports": [ "2026at", "2026w" ], "refines": [] }, "relations": [] }, { "key": "resonance-bandwidth", "label": "Resonance bandwidth", "owner": "2026av", "definition": "The width, over the perceptual dimensions, of the region in which a broadcast-a-dimension signal achieves separation between the target cohort and non-resonant observers; the degraded-broadcast-channel analogue of a capacity region. Set by the cohort's dimensional distinctiveness sin-squared-beta: a high-distinctiveness cohort has a narrow, sharp resonance bandwidth (clean self-selection), a low-distinctiveness cohort a broad one (spill toward undifferentiated reach).", "papers": { "owns": [ "2026av" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "rotation-effort-intensity", "label": "Rotation effort intensity (e)", "owner": "2026ai", "definition": "The firm's per-period investment in the knowledge-externalization loop that converts founder-bound Tier-1 brand signal into Tier-4 organizational substrate.", "papers": { "owns": [ "2026ai" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "self-selection-filter", "label": "Self-selection filter", "owner": "2026av", "definition": "The forward reading of perception-metamerism: the same off-axis perceptual distinctiveness (sin-squared-beta) that is a mis-targeting LOSS under push-targeting in the parent paper becomes, under broadcast-a-dimension, the SHARPNESS with which a dimension-strong signal sorts the responsive cohort from the rest — the targeting bug read forward as a filter. A dimension-strong creative therefore over-indexes on the dimension-sensitive cohort with magnitude increasing in that distinctiveness (resonance over-index).", "papers": { "owns": [ "2026av" ], "imports": [ "2026aw" ], "refines": [] }, "relations": [ { "type": "specializes", "target": "spectral-metamerism" } ] }, { "key": "separability-kink", "label": "Separability kink (kappa)", "owner": "2026ai", "definition": "The threshold value of Tier-4 share above which a brand asset becomes acquirable as a freestanding asset independent of the originating principal, marking a discontinuity in the marginal M&A value.", "papers": { "owns": [ "2026ai" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "signal-coherence", "label": "Signal Coherence", "owner": "2026s", "definition": "A coherence type with concentrated emission on most (5-6) dimensions so all audiences perceive essentially the same brand; exemplar IKEA.", "papers": { "owns": [ "2026s" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "signal-source-clustering", "label": "Signal-source clustering", "owner": "2026ax", "definition": "The hierarchical aggregation reflection -> source -> cohort that corrects pseudo-replication: reflections are averaged within a source (a verbatim outlet/venue, or for first-party data a respondent/wave/vendor pseudonym), then over distinct sources, and the cohort cluster-bootstrap resamples SOURCES not reflections. It is a within-cohort estimator correction on the SOURCES of signal; the unit of inference and output stays the cohort distribution, so it coexists with the corpus stance that the instrument measures cohorts, never individuals (no person is identified, reported, or stored).", "papers": { "owns": [ "2026ax" ], "imports": [], "refines": [] }, "relations": [ { "type": "contrasts", "target": "reflection" } ] }, { "key": "six-tier-ontology", "label": "six-tier ontology", "owner": "2026ag", "definition": "The ontology that decomposes an organization into six nested specification tiers, always in the order Owner Intent -> Business Model -> Business Entity -> Product -> Process -> Organization. Each tier answers a distinct governing question and transfers differently on sale.", "papers": { "owns": [ "2026ag" ], "imports": [ "2026ae", "2026af", "2026ah", "2026ai", "2026aj", "2026al", "2026am", "2026an", "2026h", "2026m", "2026u" ], "refines": [] }, "relations": [] }, { "key": "snapshot-versus-rendering", "label": "Snapshot versus rendering", "owner": "2026al", "definition": "The distinction between a snapshot (a frozen projection extracted from its substrate that can only re-render existing claims) and a rendering (a live, refreshable projection over the current log that can answer new queries).", "papers": { "owns": [ "2026al" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "specification-coherence-index", "label": "Specification Coherence Index", "owner": "2026an", "definition": "A scalable archival measure of specification readiness built from year-over-year cosine similarity of a firm's 10-K narrative embeddings, with a four-event sharp index as robustness.", "papers": { "owns": [ "2026an" ], "imports": [ "2026ay" ], "refines": [] }, "relations": [] }, { "key": "specification-maturity", "label": "Specification Maturity", "owner": "orgschema-audit", "definition": "The degree to which an organization's operations are governed by explicit, testable, traceable specifications at each cascade level, as opposed to undocumented or misaligned ones.", "papers": { "owns": [ "2026ar" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "specification-readiness", "label": "Specification Readiness", "owner": "2026am", "definition": "The degree to which a firm's commitments are codified in versioned, machine-readable, queryable form, treated as the architectural moderator of AI returns and functional friction.", "papers": { "owns": [ "2026am" ], "imports": [ "2026an" ], "refines": [] }, "relations": [] }, { "key": "spectral-brand-theory", "label": "Spectral Brand Theory", "owner": "2026a", "definition": "The theory that a brand is not a property of an object but a signal completed in the observer: an 8-dimensional spectral profile that, when received by an observer cohort, collapses into a distribution of brand convictions (a perception cloud). Brand is measured, not managed.", "papers": { "owns": [ "2026a" ], "imports": [ "2026aa", "2026ac", "2026ad", "2026ah", "2026ar", "2026as", "2026au", "2026av", "2026aw", "2026ax", "2026b", "2026c", "2026d", "2026e", "2026f", "2026g", "2026n", "2026p", "2026r", "2026s", "2026u", "2026v", "2026w", "2026x", "2026y", "2026z" ], "refines": [] }, "relations": [] }, { "key": "spectral-dimensions", "label": "the 8 dimensions", "owner": "2026a", "definition": "The eight spectral dimensions of a brand signal, in canonical order: semiotic, narrative, ideological, experiential, social, economic, cultural, temporal. Lowercase in prose.", "papers": { "owns": [ "2026a" ], "imports": [ "2026aa", "2026ac", "2026ad", "2026ae", "2026af", "2026ah", "2026ar", "2026as", "2026at", "2026au", "2026av", "2026aw", "2026ax", "2026az", "2026ba", "2026bb", "2026c", "2026d", "2026e", "2026f", "2026g", "2026h", "2026j", "2026k", "2026n", "2026p", "2026r", "2026s", "2026v", "2026x", "2026y", "2026z" ], "refines": [] }, "relations": [] }, { "key": "spectral-dynamics", "label": "Spectral Dynamics", "owner": "2026z", "definition": "A differential calculus for multi-dimensional brand perception that extends SBT's static eight-dimensional profiles to velocity and acceleration vectors and a 16-dimensional phase space.", "papers": { "owns": [ "2026z" ], "imports": [ "2026aw" ], "refines": [ "2026aw" ] }, "relations": [] }, { "key": "spectral-gap-restoration-threshold", "label": "Spectral Gap Restoration Threshold", "owner": "2026ad", "definition": "A closed-form sufficient condition for cohort separability survival after a coherence shock: the corrective coherence emission rate must exceed the spectral leakage rate at the observer cohort's detection scale.", "papers": { "owns": [ "2026ad" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "spectral-identity", "label": "Spectral Identity", "owner": "2026n", "definition": "The formalization of Aaker's brand identity as a parametrized eight-dimensional perceptual structure with observer-specific spectral weights, converting judgment-dependent identity decisions into testable, computable operations.", "papers": { "owns": [ "2026n" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "spectral-immunity", "label": "Spectral Immunity", "owner": "2026ac", "definition": "The phenomenon whereby brand portfolio interference disappears for AI observers: despite a permanently saturated awareness gate, a rate-distortion/bandwidth constraint prevents organizational-coordination context from propagating into LLM brand encodings.", "papers": { "owns": [ "2026ac" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "spectral-interference", "label": "Spectral Interference", "owner": "2026ac", "definition": "The formalized mechanism by which sibling brands under common ownership perturb each other's perceived emission profile across the eight perceptual dimensions, gated by observer awareness and channel bandwidth.", "papers": { "owns": [ "2026ac" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "spectral-leakage-rate", "label": "Spectral Leakage Rate", "owner": "2026ad", "definition": "The rate of cross-cohort perceptual mass transfer per unit time, the Frobenius norm of the off-diagonal block of the perception operator's generator under a coherence shock.", "papers": { "owns": [ "2026ad" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "spectral-metamerism", "label": "Spectral Metamerism", "owner": "2026e", "definition": "The phenomenon whereby structurally distinct brand profiles produce identical scalar evaluations, arising as a geometric inevitability of projecting the eight-dimensional spectral profile to a lower-dimensional grade.", "papers": { "owns": [ "2026e" ], "imports": [ "2026au", "2026av", "2026aw", "2026ax", "2026ay", "2026az" ], "refines": [] }, "relations": [] }, { "key": "spectral-projection-operator", "label": "Spectral Projection Operator", "owner": "2026ae", "definition": "An idempotent ($P^2=P$), self-adjoint ($P^*=P$) linear map onto an invariant subspace whose rank determines how many independent dimensions of organizational performance the verification process can discriminate.", "papers": { "owns": [ "2026ae" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "spectral-sensitivity-index", "label": "Spectral Sensitivity Index", "owner": "2026d", "definition": "An observer-weighted curvature measure derived from Jacobi-field analysis that links a brand's static geometric position to its dynamic trajectory vulnerability, with singularities at structural-absence boundaries.", "papers": { "owns": [ "2026d" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "spectral-weight", "label": "Spectral Weight", "owner": "2026n", "definition": "A cohort's per-dimension contribution coefficient across the eight dimensions; core identity elements correspond to highest-weight dimensions and extended elements to moderate-weight dimensions, making the core/extended distinction empirically discoverable.", "papers": { "owns": [ "2026n" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "spine", "label": "Spine (semantic substrate)", "owner": "2026ao", "definition": "The semantic substrate S = sigma(L): a typed directed acyclic graph extracted from the log substrate whose vertices are claims, observations, methods, findings, propositions, derivations, and rivals, with typed edges among them.", "papers": { "owns": [ "2026ao" ], "imports": [ "2026ap", "2026u" ], "refines": [] }, "relations": [] }, { "key": "spine-first-drafting-protocol", "label": "Spine-First Drafting Protocol", "owner": "2026ao", "definition": "The cost-minimizing intervention of locking the substrate before drafting prose, tracing every prose claim to a substrate entry, resolving orphan claims as fork or rebase, and evaluating substrate coherence and prose craft separately.", "papers": { "owns": [ "2026ao" ], "imports": [ "2026ap", "2026u" ], "refines": [] }, "relations": [] }, { "key": "structural-absence", "label": "structural absence", "owner": "2026a", "definition": "The absence of a designed signal on a dimension, which itself carries perceptual information (\"dark signals\" is acceptable shorthand).", "papers": { "owns": [ "2026a" ], "imports": [ "2026d", "2026e", "2026g", "2026k", "2026p" ], "refines": [] }, "relations": [] }, { "key": "substrate-as-repository", "label": "Substrate as repository", "owner": "2026u", "definition": "The realized instantiation of Research-as-Repository: a single content-addressed store unifying a corpus's terms, claims, and citations graphs as one source of truth, of which papers, glossaries, BibTeX, and other artifacts are projections (renders).", "papers": { "owns": [ "2026u" ], "imports": [ "2026at" ], "refines": [] }, "relations": [ { "type": "specializes", "target": "research-as-repository" } ] }, { "key": "substrate-floor", "label": "Substrate floor", "owner": "substrate-floor", "definition": "The dispersion of several instruments' verdicts on one aligned claim, treated as a noise floor for the cross-instrument ensemble: the operator/artifact noise-floor move lifted one level up. Across instruments, agreement is triangulation and disagreement is the floor itself; a cross-instrument finding survives only if its consensus signal clears the substrate floor.", "papers": { "owns": [ "2026ay" ], "imports": [ "2026ba" ], "refines": [] }, "relations": [ { "type": "contrasts", "target": "cross-substrate-dispersion" } ] }, { "key": "substrate-operator", "label": "Substrate-Operator vs Surface-Operator", "owner": "2026am", "definition": "An operator (human or AI) whose execution is specification-constrained and coherent across interfaces, contrasted with a Surface-Operator whose output is locally fluent but globally inconsistent because it lacks specification grounding.", "papers": { "owns": [ "2026am" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "temporal-stability-hierarchy", "label": "Temporal Stability Hierarchy", "owner": "org-as-metadata", "definition": "The ordering of three organizational layers by characteristic stability: value outputs change less frequently than processes, which change less frequently than the organizational configurations that execute them.", "papers": { "owns": [ "2026af" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "tier-1-owner-intent", "label": "Tier 1 (Owner Intent)", "owner": "2026ag", "definition": "Why the organization exists. Governed by founder / board chair / dominant shareholder; implicit or off-table in most professional-CEO companies. Transfers nothing directly, only its imprint on lower tiers.", "papers": { "owns": [ "2026ag" ], "imports": [ "2026ah", "2026ai", "2026aj", "2026am", "2026an" ], "refines": [] }, "relations": [] }, { "key": "tier-2-business-model", "label": "Tier 2 (Business Model)", "owner": "2026ag", "definition": "How value flows into resources. Governed by the CEO (founder-CEOs collapse Tier 1 into Tier 2). Conceptually replicable; not legally owned.", "papers": { "owns": [ "2026ag" ], "imports": [ "2026ah", "2026aj", "2026am", "2026an" ], "refines": [] }, "relations": [] }, { "key": "tier-3-business-entity", "label": "Tier 3 (Business Entity)", "owner": "2026ag", "definition": "What is legally registered and saleable (IP, trademarks, contracts, corporate-legal personality). Governed by General Counsel / corporate treasury. Transfers by document. Often absent from AI-strategy meetings.", "papers": { "owns": [ "2026ag" ], "imports": [ "2026ah", "2026aj", "2026am", "2026an" ], "refines": [] }, "relations": [] }, { "key": "tier-3-visibility-in-tier-4", "label": "Tier-3-visibility-in-Tier-4 parameter (V)", "owner": "2026ah", "definition": "A continuous parameter V operationalizing the Aaker-Joachimsthaler Brand Relationship Spectrum as the degree to which the Tier-3 business entity is visible in the Tier-4 brand specification.", "papers": { "owns": [ "2026ah" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "tier-4-product", "label": "Tier 4 (Product)", "owner": "2026ag", "definition": "What is delivered to whom; includes the brand surface (per Brand-as-Tier-4). CMO governs the brand sub-spec; CTO the technical sub-spec (canonical collision at Tier 4). Transfers if specified; not if tacit.", "papers": { "owns": [ "2026ag" ], "imports": [ "2026ah", "2026ai", "2026aj", "2026am", "2026an" ], "refines": [] }, "relations": [] }, { "key": "tier-4-share", "label": "Tier-4 share (s)", "owner": "2026ai", "definition": "The proportion s in [0,1] of a brand's total observable signal residing in a substrate an acquirer can hold independently of any individual.", "papers": { "owns": [ "2026ai" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "tier-5-process", "label": "Tier 5 (Process)", "owner": "2026ag", "definition": "How the product is produced. CFO governs the financial sub-spec; COO the operational sub-spec (canonical collision at Tier 5). Transfers if codified.", "papers": { "owns": [ "2026ag" ], "imports": [ "2026ah", "2026aj", "2026am", "2026an" ], "refines": [] }, "relations": [] }, { "key": "tier-6-organization", "label": "Tier 6 (Organization)", "owner": "2026ag", "definition": "Who does the producing. Governed by CHRO (sometimes COO). Transfers only partially (retention contracts at best).", "papers": { "owns": [ "2026ag" ], "imports": [ "2026ah", "2026aj", "2026am", "2026an" ], "refines": [] }, "relations": [] }, { "key": "tier-allocation", "label": "Tier allocation", "owner": "2026aj", "definition": "The cross-tier capital-allocation problem of choosing how to direct marginal investment across operating tiers that differ in substrate decay rate, yielding a closed-form allocation rule.", "papers": { "owns": [ "2026aj" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "tier-independence-overestimation", "label": "Tier-independence overestimation problem", "owner": "2026aj", "definition": "The error of attributing durable-stock value to a target whose revenue-generating assets are constitutively flow-dependent (high Tier-6), producing goodwill premiums that exceed the substrate that actually transfers.", "papers": { "owns": [ "2026aj" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "tier-rotation", "label": "Tier rotation", "owner": "2026ai", "definition": "The deliberate, multi-decade migration of brand signal from a founder-bound Tier-1 substrate into an institutionally separable Tier-4 product-brand substrate via knowledge externalization.", "papers": { "owns": [ "2026ai" ], "imports": [ "2026aj" ], "refines": [] }, "relations": [] }, { "key": "tier-rotation-curve", "label": "Tier-Rotation Curve", "owner": "2026ai", "definition": "A continuous logistic-form model of how a brand's Tier-4 share accumulates over time and a piecewise M&A value function with a discontinuous slope at the separability kink.", "papers": { "owns": [ "2026ai" ], "imports": [ "2026aj" ], "refines": [] }, "relations": [] }, { "key": "tier-specific-decay-rate", "label": "Tier-specific decay rate", "owner": "2026aj", "definition": "The per-period fraction of a tier's accumulated substrate stock that depreciates each period, architecturally determined by the tier's persistence mechanism.", "papers": { "owns": [ "2026aj" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "trajectory-clustering", "label": "Trajectory Clustering", "owner": "2026z", "definition": "Grouping brands by their dynamic state (x,v) rather than static position, enabling detection of competitive convergence and divergence before they manifest in position.", "papers": { "owns": [ "2026z" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "triangulation-resolution-criterion", "label": "Triangulation resolution criterion", "owner": "2026ax", "definition": "The decision rule for the distribution-level metric: a cohort pair is declared RESOLVED only when three independent tests agree — a Holm-corrected energy-distance permutation p < .05 AND the operator-floored distributional signal-to-noise 95%-CI lower bound > 1 AND leave-one-source-out accuracy above chance. Conservative by construction (each test fails on a different mode); guards against metric-shopping together with Holm/BH correction, a metric ensemble, and a permutation-null false-positive calibration. Because the distributional metric was chosen after the confirmatory mean-cosine null, a resolution under this criterion is reported as EXPLORATORY and pre-registered going forward.", "papers": { "owns": [ "2026ax" ], "imports": [], "refines": [] }, "relations": [ { "type": "contrasts", "target": "per-pair-resolution-criterion" } ] }, { "key": "two-window-falsification", "label": "Two-window falsification test", "owner": "2026ax", "definition": "A pre-registered structural-validity test that runs the identical instrument + battery on two sampling windows of the same case expected to differ in cross-cohort divergence. The instrument passes if it resolves the predicted-different cohort pairs on the divergent-discourse window and returns sub-resolution on a convergent-discourse window; a reversed ordering (resolving a convergent window or failing a divergent one) falsifies the discriminant claim. It demonstrates the instrument resolves real differences and refuses to manufacture absent ones.", "papers": { "owns": [ "2026ax" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "type-over-score-principle", "label": "Type-over-Score Principle", "owner": "2026s", "definition": "The result that crisis survival depends on the minimum drift across dimensions (the shape of the emission profile) rather than its total magnitude, so coherence type predicts resilience better than coherence score.", "papers": { "owns": [ "2026s" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "value-headroom", "label": "Value Headroom", "owner": "negotiation_spec_2026", "definition": "The fraction of attainable joint value a naively cooperative pair would leave on the table, operationalized as (Pareto-joint minus naive-joint) over Pareto-joint, which moderates whether specification beats style.", "papers": { "owns": [ "2026aq" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "value-layer", "label": "Value Layer", "owner": "org-as-metadata", "definition": "The layer consisting of the outputs a productive activity is intended to deliver, defined from the perspective of the evaluative observer who assesses them.", "papers": { "owns": [ "2026af" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "verification-as-operator", "label": "Verification as Operator", "owner": "2026ae", "definition": "The formalization of organizational verification as a spectral projection operator P that maps organizational states onto invariant subspaces defined by acceptance criteria.", "papers": { "owns": [ "2026ae" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "verification-bandwidth", "label": "Verification Bandwidth", "owner": "2026ae", "definition": "The maximum number of independent specification conditions an organization can evaluate per verification cycle, which bounds the projection rank it can sustain at steady state.", "papers": { "owns": [ "2026ae" ], "imports": [], "refines": [] }, "relations": [] }, { "key": "version-epoch", "label": "Version epoch", "owner": "2026ba", "definition": "One rung of the model-version ladder: a real, shipped vendor version under which the panels are read (labelled VE-). Epochs are added only when a vendor ships a real version - synthetic versioning (fine-tunes, quantizations, prompt variants) is excluded by protocol. For a pinned panel the reading depends on (artifact bytes, prompt bytes, model version) only, so already-shipped back-catalog versions constitute valid epochs.", "papers": { "owns": [ "2026ba" ], "imports": [ "2026ax" ], "refines": [] }, "relations": [] }, { "key": "version-floor", "label": "Version floor", "owner": "2026ba", "definition": "The reliability band for longitudinal LLM measurement: the dispersion across model versions of a family reading a byte-identical artifact panel under a matched extractor - the across-time counterpart of the operator floor. Because the pinned input cannot have changed, the version floor is a pure apparatus-drift band; a longitudinal 'the brand moved' claim must clear it, not merely the contemporaneous operator floor (floor nesting: operator within version).", "papers": { "owns": [ "2026ba" ], "imports": [ "2026ax" ], "refines": [] }, "relations": [ { "type": "specializes", "target": "operator-noise-floor" } ] } ], "citation_edges": [ { "from": "2026a", "to": "2026aa", "role": "applies", "criticality": "supportive" }, { "from": "2026a", "to": "2026ad", "role": "applies", "criticality": "supportive" }, { "from": "2026a", "to": "2026ad", "role": "tests", "criticality": "supportive" }, { "from": "2026a", "to": "2026b", "role": "unclassified", "criticality": "supportive" }, { "from": "2026a", "to": "2026d", "role": "applies", "criticality": "supportive" }, { "from": "2026a", "to": "2026e", "role": "applies", "criticality": "critical" }, { "from": "2026a", "to": "2026f", "role": "applies", "criticality": 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