# Canonical research corpus

This directory is the source-of-truth research record. It is intentionally distinct from the curated books and generated website.

The [generated corpus front door](FRONT_DOOR.md) maps this interior through declared roots, exact authority and provenance labels, capability-specific minimum closures, link reachability and an explicit classification for every object in the canonical inventory. Use it when the question is not merely “where should I start?” but “what is here, how is it connected, and what would a bounded subset omit?”

The [generated evidence spine](EVIDENCE_SPINE.md) is the claim-level drill-down beneath that map. It preserves canonical and observed file identity, exact declaration and link locations, certificate/evidence joins, scoped verdict text, marked title inferences and inbound consumer candidates. Missing joins remain visible; backlinks are not treated as endorsement, and structural indexing never promotes scientific status.

For a question rather than a declared entrance, run the repository's [hybrid corpus search](../tooling/search/search_corpus.mjs). Weighted lexical retrieval supplies the query signal; personalized PageRank follows the corpus's actual links to recover surrounding context; and a selector sweep exposes dependence on the navigation prior. Results retain declared status and remain navigation aids, never evidence or epistemic promotion.

```powershell
node tooling/search/search_corpus.mjs --query "Casimir boundary response"
```

## The current story

The corpus is organized around an invariant relation rather than a single
symmetry slogan. Its non-negotiable explanatory order is **Jordan admission and composition → typed admissibility region** (the living carrier and its admissible relations) **→ locally invariant carrier → Lie transformation and transport** of thing and mirror face **→ holonomy, dynamics, selection and records**. In the central exact model,
\(M^T\Omega M=\Omega\): \(M\) moves the living carrier, \(M^{-T}\) is its
mirror face, and \(\Omega\) carries their persistent local comparison. The
exterior-square relation space then separates as
\(\Lambda^2V^*=\mathbb R\Omega\oplus\Lambda^2_0V^*\); its five-dimensional
primitive remainder carries the signature-\((2,3)\) geometry behind
\(Sp(4,\mathbb R)\cong Spin_0(2,3)\). This is an exact theorem about a declared
carrier and its relations, not a declaration that either space is physical
spacetime. Read the [canonical reading contract](READING_CONTRACT.md), the
[locally invariant carrier spine](programmes/admissibility/admissibility_123_locally_invariant_carrier_and_mirror_face_spine.md)
and the [explanatory standard](EXPLANATORY_STANDARD.md) before interpreting
any group-centred branch.

The admissibility programme turns that question into an atlas. It tracks what is mathematically filled, conditionally constructed, excluded, bounded, underidentified, experimentally inaccessible and still uncharted. Dynamics remains essential, but no longer enters as an unexplained sovereign: it must preserve or transform an admitted domain and leave records by which competing mechanisms can be separated.

Start with [The admissibility frontier: the current story of the corpus](syntheses/the_admissibility_frontier_current_synthesis.md). It is the reader-facing synthesis of what has been found, what it means, why the programme remains hopeful, where the live edges are and how to join without surrendering the corpus's kenotic authority boundaries.

To enter through a concrete task, use [Start here by role](START_HERE_BY_ROLE.md), the [working glossary](GLOSSARY.md) and the repository [contribution guide](../CONTRIBUTING.md).

## Contents

- [`claims/`](claims/README.md) — the numbered, append-only research ledger;
- [`syntheses/`](syntheses/) — large interpretive and thesis-scale documents;
- [`programmes/`](programmes/) — coordinated branches, waves and closure exercises;
- [`governance/`](governance/) — repository history and publication state;
- [`registers/`](registers/) — manifests, audits and machine-readable programme state.

## Foundational programmes

- [Programme Algebra parallel lane](programmes/programme-algebra/README.md) — compiles every corpus document and authored section into a hash-bound twelve-coordinate epistemic kernel, preserves explicit documentary relations without promoting them to scientific transformations, and admits only common-algebra paths with exact endpoint, dimension, assumption, loss, evidence and authority receipts. It remains a reversible non-replacing lane until held-out retrieval, reasoning and human-reading gates justify migration.

- [Dynatology](programmes/dynatology/README.md) — the corpus-wide ontology of structured possibility, admissibility, reachability, selection, realization, dynamics, observation, quotient scars and scale/composition; includes a [canonical ontology](programmes/dynatology/dynatology_00_ontology_and_scope.md), [investigation protocol](programmes/dynatology/dynatology_01_investigation_protocol.md), [corpus crosswalk](programmes/dynatology/dynatology_02_corpus_crosswalk.md) and machine-readable register.

- [Governed mystery atlas](programmes/dynatology/mystery_atlas_00_governance_and_claimipedia_reconciliation.md) — an extensible evidence-neutral lane for unresolved and esoteric questions, with dedicated maps for [consciousness, Orch OR, Schumann/EEG and anomalous cognition](programmes/dynatology/mystery_atlas_01_consciousness_and_brain_environment.md), [pyramids, megaliths and hidden-physics claims](programmes/dynatology/mystery_atlas_02_ancient_structures_and_hidden_physics.md), an [initial corpus collision investigation](programmes/dynatology/mystery_atlas_03_initial_corpus_investigation.md), a [deep five-coordinate distance audit of every target](programmes/dynatology/mystery_atlas_04_deep_distance_to_corpus.md), a foundational [sacred-geometry bridge](programmes/dynatology/mystery_atlas_05_sacred_geometry_bridge.md), a [muqarnas plan-to-vault comparison with octonionic generative structure](programmes/dynatology/mystery_atlas_06_muqarnas_octonion_generative_bridge.md), its exact [symbol-collapse versus geometric-action compiler boundary](programmes/dynatology/mystery_atlas_07_muqarnas_compiler_boundary_and_source_packet.md), the first [Topkapı drawing 108 multiplex pretranscription](programmes/dynatology/mystery_atlas_08_topkapi_108_multiplex_pretranscription.md), the [recovered radial generator](programmes/dynatology/mystery_atlas_09_topkapi_108_radial_generator.md), a [mathematics literature and novelty review](programmes/dynatology/mystery_atlas_10_muqarnas_mathematics_literature_review.md), the selected [typed rewriting and operadic compiler formalism](programmes/dynatology/mystery_atlas_11_muqarnas_formalism_and_toy_compiler.md), the source-derived [Topkapı lift fibre and boundary adapter](programmes/dynatology/mystery_atlas_12_topkapi_lift_fibre_and_boundary_adapter.md), the four-plan [scaffold--plan--realization fibre tower](programmes/dynatology/mystery_atlas_13_topkapi_scaffold_fibre_tower.md), the [golden ratio as the local fivefold module](programmes/dynatology/mystery_atlas_14_golden_ratio_local_module.md), and verified machine-readable coverage, collision, distance, motif, bridge and source registers.

- [Admissibility foundations](programmes/admissibility/admissibility_00_foundational_programme.md) — asks whether admissibility can generate physical structure rather than merely constrain an already specified theory. Its present explanatory spine is [the locally invariant carrier and its mirror face](programmes/admissibility/admissibility_123_locally_invariant_carrier_and_mirror_face_spine.md): \(M^T\Omega M=\Omega\) joins direct and dual perspectives, compatible transport separates local invariance from global holonomy, and the primitive exterior-square remainder generates the five-dimensional signature-\((2,3)\) relation space. The programme begins from [Casimir invariants](programmes/admissibility/admissibility_02_casimir_as_first_generative_probe.md), maps [dispersion forces](programmes/admissibility/admissibility_04_dispersion_force_landscape.md), [invariants](programmes/admissibility/admissibility_05_invariant_atlas_time_force_measure_material_rotation.md), [dynamic response and detection](programmes/admissibility/admissibility_06_dynamic_response_geometry_detection_metastability.md), and develops the exact carrier, selector, holonomy and experimental branches linked from the canonical spine.

- [Relation--face compiler](programmes/admissibility/admissibility_124_relation_face_compiler_from_adjacency_to_jordan_holonomy.md) — turns adjacency into a typed generative route: rank-one edge kernels sew into positive Laplacians, Schur elimination compiles hidden paths into a two-port Jordan face, cycle rank identifies when complex phase becomes gauge-invariant, and an orientation-odd detector lifts the mirror pair discarded by the cubic determinant.

- [Claimipedia support-native order boundary](programmes/admissibility/admissibility_125_claimipedia_support_native_order_and_semantic_boundary.md) — executes that compiler on the live captured relation source: incidence gives a canonical positive kernel and exact Spin--Temple face, but erases arrow direction and every relation type; the source-native river dependency triangle becomes the nearest honest loop-closure experiment once real maps and held-out data replace fixtures.

- [Transition operators, selection rules and lifetimes](programmes/admissibility/admissibility_127_transition_operators_selection_rules_and_lifetime_frontier.md) — supplies the previously missing bridge from rotational classification through a physical transition operator, reduced matrix element and phase space to partial width, lifetime and detector record; metastable helium and distinct nuclear gamma, beta and alpha mechanisms provide the worked cases and an operator-opening experiment.

- [Widths, coherence and escape are not one lifetime](programmes/admissibility/admissibility_128_widths_coherence_and_escape_are_not_one_lifetime.md) — separates population relaxation, homogeneous dephasing, static spread, power broadening, effective pole damping, detector convolution and barrier escape; a joint survival/Ramsey/echo/drive/resolution experiment tests the decomposition without refitting each spectrum.

- [Transition-operator propagation audit](programmes/frontier-physics-targets/transition_operator_propagation_audit_v1.md) — applies that boundary across all 2,226 corpus Markdown documents, records explicit semantic exclusions instead of inserting atomic jargon into unrelated mathematics, and closes the current operator/rate review queue at zero while leaving effective-spectral and barrier-metastability mechanisms separately typed.

- [Typed two-rail positive lift](programmes/admissibility/admissibility_126_typed_two_rail_positive_lift_preserves_the_mirror_face.md) — shows that positivity need not erase the relation: a 304-dimensional free source/target-and-type carrier reconstructs all 41 distinct directed typed records, realizes arrow reversal as a rail-swap mirror, and identifies the ordinary rank-33 Laplacian as an eight-direction quotient scar.

- [Complex, split-complex and dual-number local alphabet](programmes/admissibility/admissibility_129_elliptic_hyperbolic_parabolic_local_alphabet.md) — places rotation, boost/squeeze and shear in the exact family \(\mathbb R[u]/(u^2-\kappa)\). It proves that the discrete rail swap is anti-symplectic while the same matrix generates a symplectic hyperbolic flow, and identifies the square-zero dual branch as the first-order contraction seam rather than another rotation.

- [Quarter-turn and mirror generate the dual seam](programmes/admissibility/admissibility_130_quarter_turn_and_mirror_generate_the_dual_seam.md) — proves that an anticommuting complex quarter-turn and split mirror generate \(Cl(1,1)\cong M_2(\mathbb R)\), with the two dual-number rungs \((J\pm I)/2\) arising as null directions rather than imported third structures.
- [Authored rail grading closes the local Clifford cell](programmes/admissibility/admissibility_131_the_authored_rail_grading_closes_the_local_clifford_cell_but_opens_a_coincidence_channel.md) — derives the missing negative-square operator from Claimipedia's source/target grading, proves the dual rungs are canonical rail transfers and shows why the quarter-turn opens a co-incidence channel instead of preserving the incidence response.
- [Cross-corpus Clifford-cell atlas](programmes/admissibility/admissibility_132_cross_corpus_clifford_cell_atlas_and_exhaustion.md) — identifies four exact real-linear realizations, separates antiunitary and lone-nilpotent neighbours, and closes the corpus-wide semantic propagation queue without claiming a shared physical mechanism.
- [Incidence/co-incidence topology doublet](programmes/admissibility/admissibility_133_the_incidence_coincidence_doublet_detects_odd_cycle_topology.md) — shows that the two positive rail responses descend to the ordinary and signless Laplacians; their rank difference exactly counts the two odd-cycle components in the captured graph.
- [Semantic-adjoint exhaustion](programmes/admissibility/admissibility_134_no_global_semantic_adjoint_exists_on_the_current_claimipedia_relation_source.md) — exhausts all 24 relation-type permutations and 10 involutions, proving that only the two-record Spin–Temple cell reverses semantically while 41 records remain unmatched.
- [Three-resonator parity-switch detector](programmes/admissibility/admissibility_142_a_three_resonator_parity_switch_turns_the_dual_face_into_a_detector.md) — gives the carrier–selector–detector grammar a minimal physical embodiment: loop parity leaves the first two spectral invariants fixed but shifts the cubic pole product by exactly $4\kappa_{12}\kappa_{23}\kappa_{31}$.
- [A seam changes continuations but does not trigger decay](programmes/admissibility/admissibility_135_a_seam_changes_continuations_but_does_not_by_itself_trigger_decay.md) — separates local seam crossing, independently supplied transition channels and collapse; retains the W/Z reading as a falsifiable conditional conjecture requiring a physical embedding and a channel-specific record.
- [Observer, horizon and channel atlas](programmes/admissibility/admissibility_140_observer_horizon_channel_atlas_and_exhaustion.md) — adds the previously light Unruh, Hawking, full-Kerr and nuclear open-system frontiers. Five packets distinguish observer-relative detector response, horizon geometry, ergosurfaces, superradiant thresholds, transition channels and records; each ends in a go/no-go programme rather than a shared-word identification.
- [Observer, horizon and nuclear literature review](programmes/frontier-physics-targets/observer_horizon_nuclear_literature_review_v1.md) — states what the conventional source literature licenses and, equally importantly, what it does not license for the Jordan–Lie programme.
- [Priority for the next observer/horizon/nuclear insight](programmes/admissibility/admissibility_141_observer_horizon_and_nuclear_priority_for_next_insight.md) — separates conceptual importance from experimental leverage and ranks a controlled (^{229})Th host/channel factorization and public Kerr multi-record analysis as the next paired work.
- [Thorium-229 shared-parent/host-channel factorization](programmes/admissibility/admissibility_143_th229_shared_parent_host_channel_factorization_programme.md) and [GW250114 Kerr multi-record consistency](programmes/admissibility/admissibility_144_kerr_multirecord_public_data_consistency_programme.md) — make that pair executable with public inputs, frozen predictive splits and separate build, bridge, physics and propagation gates. The current ledger supplies no Jordan/Spin bridge and permits no automatic new-physics promotion.
- [Bulk-cone resolution and the exact-record gate](programmes/admissibility/admissibility_145_bulk_cone_resolution_exact_correlators_overrule_sharp_semiclassical_geometry.md) — integrates the finite-\(G_N\) holographic no-go: OPE convergence and joint time/temperature analyticity remove a sharp semiclassical bulk-cone singularity, while a finite-central-charge calculation replaces it by a broadened peak. This supplies a reusable test for whether an emergent geometric feature survives as an exact detector record, without treating AdS\(_5\) or AdS\(_3\) as a direct Spin(2,3) bridge.
- [Multilinear Kakeya transversality gate](programmes/admissibility/admissibility_146_multilinear_kakeya_transversality_bounds_collective_carrier_concentration.md) — turns directional independence into a quantitative bound on collective tube overlap across scale. In three dimensions its trilinear occupancy detector and wedge-determinant conditioning give an exact, bounded realization of “three relations detect structure,” while the physical wave-packet dictionary and any Spin(2,3) identification remain open.
- [Xi genus two, Weil spectral compression and hyperbolic traces](programmes/admissibility/admissibility_147_xi_genus_two_weil_spectral_compression_and_hyperbolic_trace_gate.md) — separates three arithmetic record mechanisms: a logarithmic derivative makes a conjugate Xi product additive, compressed self-adjoint inverses yield finite spectra converging to zeta ordinates under RH, and hypersurface traces turn automorphic Green kernels into finite geometric records. The genus-two and certificate claims remain behind marked-carrier, assumption and replay gates.
- [Lithium niobate: a crystal that makes relations physical](programmes/admissibility/admissibility_148_lithium_niobate_as_a_relational_physics_workbench.md) — maps one established multi-physics material into independently calibrated carriers, selectors, dynamics, memory and detector records. It separates quadratic frequency mixing from logarithmic product-to-sum transforms and proposes a same-device phase-closure experiment without promoting an engineered emulator into fundamental ontology.

- [Regulus closure bridge](programmes/regulus-closure-bridge/README.md) — reconstructs the finite \(E_6\) incidence hierarchy from the 40-point \(Spin(2,3)\) shadow, realizes the 36 double-sixes as explicit complete two-qutrit stabilizer-MUB frames, compresses their invariant dynamics to a three-sector Hecke/Bose–Mesner algebra, derives selector and lift obstructions, and specifies the nearest frame-preserving experiment.

- [Admissibility robustness window](programmes/admissibility/admissibility_27_robustness_window_for_projective_return_coherent_holonomy_and_selection.md) — separates projector closure, coherent quarter-turn, nonunitary loss distortion and genuine return-map contraction into four independently testable channels, and derives their simultaneous timing, degeneracy and noise budget.

- [Quarter-turn platform triage](programmes/admissibility/admissibility_28_platform_triage_for_the_quarter_turn_contraction_experiment.md) — compares primary-source integrated-photonic, atomic, synthetic-frequency and superconducting holonomy demonstrations against that typed budget; no platform is yet admitted, integrated silicon nitride is the closest carrier, and Rb-87 supplies the closest reversal-and-tomography protocol.

- [Seebeck and anomalous Nernst guideposts](programmes/admissibility/admissibility_29_seebeck_nernst_guideposts_for_response_geometry.md) — places longitudinal spectral sensitivity and transverse orientation-odd thermoelectric response inside the admissibility map, with full tensor unmixing, Onsager reversal, Mott, frequency and hysteresis controls.

- [Casimir--Seebeck--Nernst spectral ladder](programmes/admissibility/admissibility_30_casimir_seebeck_nernst_spectral_ladder.md) — adds global boundary-conditioned fluctuation response to the longitudinal and transverse transport guideposts while keeping representation Casimirs, the Casimir effect and Onsager--Casimir reciprocity rigorously distinct.

- [Same-carrier Casimir--thermoelectric platform closure](programmes/admissibility/admissibility_31_same_carrier_platform_closure_for_casimir_thermoelectric_response.md) — identifies Co2MnGa as the closest material carrier, the demonstrated birefringent Casimir torque as the closest force protocol and Weyl-semimetal scattering theory as the bridge, while locating the missing broadband off-diagonal tensor and matched-film no-refit prediction.

- [Wide frontier atlas and iterative research queue](programmes/admissibility/admissibility_32_wide_frontier_atlas_and_iterative_research_queue.md) — regroups the full corpus into fourteen observable-facing lanes, scores them by reach, falsifiability, null utility and bridge risk, and establishes a five-packet execute/zoom-out/re-rank workflow.

- [Hybrid bosonic carrier and adversarial thermal-Hall frontier](programmes/admissibility/admissibility_33_hybrid_bosonic_carrier_and_adversarial_thermal_hall_frontier.md) — separates a controlled acoustic non-Abelian emulator from a material-response inference branch, identifies a photon–magnon–phonon triple as the closest literal hybrid carrier, and makes Berry-curvature versus many-body-skew thermal Hall a detector-equivalence test.

- [Physical energy-current construction gate](programmes/admissibility/admissibility_34_physical_energy_current_construction_gate.md) — derives the energy current from the code's own geometrically tagged Hamiltonian terms, proves the local continuity and current-graph identities in an executable witness, and isolates periodic seam, energy-density gauge and FTLM implementation as the remaining finite tasks.

- [Adversarial detector-equivalence atlas](programmes/admissibility/admissibility_35_adversarial_detector_equivalence_atlas.md) — defines exact detector equivalence after nuisance projection, maps eight mechanism collisions across the active frontiers, and selects added reversal, frequency, geometry, waiting-time or higher-moment channels by conditional information per cost.

- [Frontier expansion: cost, backaction, scale and rare events](programmes/admissibility/admissibility_36_frontier_expansion_cost_backaction_scale_and_rare_events.md) — adds seven underweighted process frontiers: thermodynamic cost, measurement backaction, scale stability, rare events, complexity, causal speed and disorder/glassy memory.
- [Frontier physics target set](programmes/frontier-physics-targets/README.md) — canonical 22-target navigation lane with [individual corpus assessments](programmes/frontier-physics-targets/frontier_physics_target_assessments_v1.md), legacy, external-validation, speculative, terminal-gate, admissibility-packet and quotient-scar crosswalks.

- [Lattice-subroutine and gravity programme](programmes/lattice-subroutine-gravity/README.md) — a MECE audit of the proposed lattice/computation route through Leech, Monster, genus-two sewing, oriented modular lines, Jordan positivity and induced gravity. The current result separates an exact finite orientation shadow from failed line-bundle and Jordan-boundary identifications, then converts the surviving distinction into a phase-sensitive three-mode transfer experiment with a strict no-refit new-physics gate.

- [Quotient-scar admissibility lane](programmes/quotient-scars/README.md) — develops the graph, composition, memory, topology and detector calculus through a 27-relation exceptional audit, derives a source-native five-type path pairing whose unique index-eight glue completion is the odd unimodular \(Spin(2,3)\)-type lattice, and executes the remaining operator bridge: the formal quiver representation succeeds, but the natural intertwiner and \(Spin(2,3)\) dynamical closure fail while a minimal directed-network detector remains exactly testable.

- [Selector contraction does not determine thermodynamic cost](programmes/admissibility/admissibility_37_selector_contraction_does_not_determine_thermodynamic_cost.md) — proves with an exact detailed-balance selector that a unique contractive fixed point can have zero stationary entropy production, and upgrades the proposed experiment to trajectory, activity, heat, reset and conditioned/unconditional measurements.

- [Measurement creates branches, not unique unconditional selection](programmes/admissibility/admissibility_38_measurement_creates_branches_not_unique_unconditional_selection.md) — proves that weak measurement can purify individual records while leaving every diagonal population state fixed in the ensemble, and shows exactly where an independently oriented damping or feedback datum enters.

- [Periodic physical energy-current bridge](programmes/admissibility/admissibility_39_periodic_physical_energy_current_bridge.md) — closes an oriented minimum-image current convention on an interacting periodic witness, including seam, translation, continuity, repartition and positive two-current checks, while leaving source-native two-dimensional FTLM integration open.

- [Planckian two-current execution tranches and literature review](programmes/admissibility/admissibility_40_planckian_two_current_execution_tranches_and_literature_review.md) — orders the remaining FPT-004 work from production term provenance through convention collision, FTLM validation, rank mapping and thermoelectric adjudication, with primary-literature anchors and explicit stop conditions.
- [Screened finite-q order-of-limits ladder](programmes/admissibility/admissibility_46_screened_finite_q_order_of_limits_ladder.md) — collides unscreened, fixed-screening and size-scaled-screening current gauges, isolating source-complete fixed-density moments as the remaining FPT-004 admission gate.
- [Source-complete finite-q gauge ladder](programmes/admissibility/admissibility_47_source_complete_finite_q_gauge_ladder.md) — restores spin and all audited t, t', J, J' and V families; their exact dilute ladder returns to quadratic gauge convergence after the small-size crossover.
- [Matrix-free fixed-density moment convergence](programmes/admissibility/admissibility_48_matrix_free_fixed_density_moment_convergence.md) — crosses exponentially large balanced one-hole sectors by stochastic column moments and closes the screened finite-q equal-time gauge gate through L=9.
- [Fixed-density block/cross rank boundary](programmes/admissibility/admissibility_49_fixed_density_block_cross_rank_boundary.md) — supports a gauge-convergent rank-two integrated response while isolating low-frequency thermodynamic rank as the surviving spectral frontier.
- [Frequency-moment bounds and compute boundary](programmes/admissibility/admissibility_50_frequency_moment_bounds_and_compute_boundary.md) — finds nondiverging generalized RMS scales and specifies the compiled typicality/KPM implementation required to reopen the low-frequency frontier.
- [Spectral boundary dynamics](programmes/admissibility/admissibility_51_spectral_boundary_dynamics_free_bloch_efimov_casimir.md) — replaces a bound/free binary by free, Bloch/interface, resonance, threshold, Efimov and discrete-bound strata; joins them through spectral shift and Wigner--Smith delay while keeping Casimir meanings, Spin(2,3) binding and the biblical “Fall” analogy behind explicit type firewalls.
- [Spectral flow and pole trajectories](programmes/admissibility/admissibility_52_spectral_flow_pole_trajectories.md) — executes the first continuum--SSH-rail--local-level sweep, follows a bound branch through continued-sheet resonance and back, measures phase, delay, localization and a scalar Casimir proxy, and records that the uncorrected phase winding is not yet a Levinson index.
- [Boundary lift to a Casimir/thermoelectric compiler](programmes/admissibility/admissibility_53_boundary_lift_to_casimir_thermoelectric_compiler.md) — proves the detector fibre-factorization criterion and exhausts a 35-placement response model in which an orientation-sensitive boundary probe restores information erased by symmetric transport.
- [Transverse detector symmetry ceiling](programmes/admissibility/admissibility_54_transverse_joint_detector_symmetry_ceiling.md) — adds a reciprocal Nernst-like channel and shows that the detector family exactly saturates, but cannot exceed, its apparatus reflection quotient.
- [Finite-band Levinson and pole collisions](programmes/admissibility/admissibility_55_finite_band_levinson_and_adaptive_pole_collisions.md) — closes the background-corrected finite-chain phase/count ledger and adaptively certifies both band-edge pole continuations.
- [Certificate-preserving descent and commuting-square atlas](programmes/admissibility/admissibility_56_certificate_preserving_descent_and_commuting_square_atlas.md) — proves the kernel-invariance criterion for autonomous quotient dynamics, composes descent defects, tests nonlinear detector lifts and places five current research signposts behind explicit certificate and loss ledgers.

- [Planckian two-current execution and convention boundary](programmes/admissibility/admissibility_41_planckian_two_current_execution_and_convention_boundary.md) — executes AZ-040 against the production source, closes provenance and admission-cluster estimator gates, finds strong periodic-current convention dependence in the held-out rank atlas, and adjudicates the result as a useful numerical extension with physical rank unresolved.

- [Ewald image cohomology and block-cross boundary](programmes/admissibility/admissibility_42_ewald_image_cohomology_and_block_cross_boundary.md) — resolves minimum image versus seam into cycle and exact graph sectors, reconstructs the production Ewald kernel from 3,267 image/reciprocal components, falsifies a real-image-only thermal twist, and validates a native block/cross estimator while withholding the rank atlas pending the reciprocal compensator.

- [Coulomb twist differentiability and finite-q boundary](programmes/admissibility/admissibility_43_coulomb_twist_differentiability_and_finite_q_boundary.md) — derives and validates the Poisson-dual reciprocal compensator on a convergent control, proves that the production two-dimensional 1/r zero mode has no uniform image-twist derivative, closes the exact reciprocal-density Hamiltonian, and redirects the transport gate to finite q or a screened order of limits.

- [Finite-q energy-continuity kernel and gauge boundary](programmes/admissibility/admissibility_44_finite_q_energy_continuity_kernel_and_gauge_boundary.md) — closes the real/reciprocal interaction-energy identity at every 3x3 wavevector and admits exact longitudinal continuity currents in declared centre and endpoint gauges, while measuring a large finite-size gauge separation that requires a size ladder before transport interpretation.

- [Finite-q odd-torus gauge ladder](programmes/admissibility/admissibility_45_finite_q_odd_torus_gauge_ladder.md) — executes an exact dilute Ewald surrogate through L=3,5,7,9 and finds centre/endpoint current separation consistent with q-min squared, promoting long-wavelength gauge convergence to a supported hypothesis while retaining the production-density gate.

The numbered filename is the stable historical identity of a claim. Folder placement is only storage sharding and does not alter that identity or its epistemic status.

## Controlling maps

- [Research document map](claims/0000-0099/00_research_document_map.md)
- [Current frontier](claims/0000-0099/30_research_frontier.md)
- [Grand synthesis](claims/0000-0099/40_grand_synthesis_spin23_pole.md)
- [Branch registry](claims/0000-0099/49_multi_branch_research_registry.md)
- [Active evidence log](claims/0000-0099/91_multi_branch_active_goal_log.md)