--- name: pick-invariant description: > Default first-line, domain-agnostic meta-reasoning control for choosing the right path. Use it to resolve an undecided choice, narrow an exploration, audit an invariant, investigate an owner-identified gap, or determine whether a validated owner can be used directly when no Pick exploration or audit is requested. Preserve target, authority, and semantics; retain only observable distinctions that can change the target decision; prefer the cheapest sufficient observation or representation; refine only on an explicit witness; and load specialist doctrine only when its trigger is material. --- # PickInvariant Govern every path by: > **Preserve target, authority, and semantics. Keep only decision-relevant distinctions. Prefer the > cheapest sufficient observation/representation. Refine only on an explicit witness.** Pick remains the structural grammar: ```text R_P(x)= ; D(x)=d(R_P(x)) ``` `P` = applicability/authority/observable scope; `I` = owned local semantics; `B` = material seams; `χ` = genuinely non-local structure. Pick locates candidate distinctions; retention is target-relative: ```text x1 ~D x2 iff no admissible target-relevant discriminator requires different decisions R(x1)=R(x2) => D(x1)=D(x2) ``` Use the coarsest evidence-supported observable representation. Retain a distinction only if removing or merging it collapses an acceptance-changing contrast or violates a bound requirement. ## 1. Authority and mode Bind supplied artifact identity before exact-conformance claims; else mark `INFERRED_PICKINVARIANT`. ```text explicit authority > validated owner > validated extension > PickInvariant derivation > preference ``` Choose one primary mode: - **BYPASS**: adequate validated owner; no requested Pick exploration/audit. Run owner directly. - **PICK_EXPLORE**: explicit open exploration; non-authoritative. No audit pass, `Δ`, mutation, rebind, or authority installation. - **PICK_AUDIT**: explicit read-only stress test; preserve owner authority and bind audit depth. - **PICK_DERIVE**: only `NO_OWNER` or owner/higher-authority adopted `PROCEDURE_GAP`; bind `INVESTIGATE | COMPILE`. Only `COMPILE` may authorize action from a complete adopted gap. Exploration/audit evidence never creates derivation authority. ## 2. Discovery, depth, and presentation Exploration may reframe broadly while anchoring target, authority, observations, and constraints. Commit only target-bound observable contrasts, falsifiable questions, or adopted gaps. The theorem stack is **internal control logic, not mandatory user-facing ceremony**. Unless architecture is requested or explanatory, answer in native domain language; do not dump `P/I/B/χ`, quotient classes, theorem names, certificates, or receipts merely to show work. Depth: - **DIRECT**: validated owner/native mechanism; default for known structure. - **FAST_DELTA**: authorized derivation with one directly evidenced observable distinction, known decision effect, no role ambiguity, and no residual interaction; use owner + smallest `Δ`. - **STRUCTURAL**: role unknown, merge collapses a contrast, seams interact, information/history/time is nontrivial, or local facts + direct boundaries cannot reconstruct `D`. - **COVERAGE**: breadth obligation only for `DELTA_AUDIT`, `FULL_AUDIT`, or another explicit completeness claim. Every escalation names its witness and new decision power; de-escalate once a simpler sufficient representation survives the relevant contrasts. Specialist probability/composition gates are orthogonal to depth unless they expose structural uncertainty. ## 3. Audit and structural commitment For `PICK_AUDIT`, bind exactly `FOCUSED_AUDIT | DELTA_AUDIT | FULL_AUDIT`. Delta/full use `SURVEY -> MAP -> CONTRAST -> PINPOINT` until each material semantic family is `CHECKED | EXCLUDED(reason) | UNVERIFIED(risk)` or a named oracle blocks progress. Separate finding confidence from completeness; reconcile stale/resolved findings; never globalize scoped `NO_GAP_FOUND`. Before structural derivation/rebinding bind domain, target, oracle, observables, exclusions, and `Q_D`; mark needed observables `AVAILABLE_NOW | PROSPECTIVE_ONLY | ERASED_UNRECOVERABLE`. For each candidate distinction ask: admissible/reachable? target/consumer-changing? observable at decision time? does removal/merge collapse a valid contrast? Retain only if needed. Preserve seam coverage `producer_guarantee >= consumer_requirement`. Prove sufficiency before minimality; reserve `MINIMAL` for target-relative removal/merge-tested claims, else use `SUFFICIENT` or `VALID_COMPRESSION`. When stochastic information-channel equivalence is material, use Blackwell/Le Cam rules in the probability/decision-quotient references; do not equate coordinate equality with information equality. When a global conclusion combines overlapping pieces, repeated decompositions, or non-local compatibility, activate `COMPOSITION_TRIGGER`; do not assume additivity. A validated owner that owns the law/composition stays `DIRECT`. ## 4. Hard specialist firewalls Activate `PROBABILITY_MEASURE_TRIGGER` only when probability law, sampling, conditioning/rejection, quotient weighting, stochastic transport, or information-channel semantics can change the target. Then **load `references/probability_semantics.md` before any law-level, `UNIFORM`, stochastic- sufficiency, conditioning, transport, canonicality, or quotient-weighting claim**. Incidental stochastic vocabulary does not fire it; a validated owner that already binds the material law may remain `DIRECT`. Null/measure-zero or parameterization-sensitive conditioning requires an explicit conditioning / disintegration basis; symmetry-based canonicality requires the invariant-measure gate. If required detail cannot load, narrow/downgrade the claim rather than inventing semantics. When several authorized observations could resolve uncertainty, prefer the cheapest reachable one that separates leading acceptance-changing alternatives; do not invent numeric priors/utilities. If a failed contrast may be abstraction-induced, validate it against raw/admissible state: real witness -> gap/failure evidence; spurious witness -> smallest witness-backed representation refinement. Never patch a known-insufficient representation only in the decision rule. ## 5. Commit and stop Only `PICK_DERIVE` may run: ```text DELTA -> OBSERVE -> COMPILE -> FREEZE -> VERIFY -> REBIND -> STOP ``` Preserve mature-owner safeguards. Every nontrivial action must prospectively resolve/discriminate a named acceptance-changing condition. Executors consume compiled artifacts and do not rediscover PickInvariant. Rebind only on observed decision misclassification plus a named missing structural distinction. The certified gap is the derivation budget. Use `PICK_LITERAL` only for an appropriate lattice polygon: `A = I + B/2 - 1`; otherwise `PICK_STRUCTURAL`. Never transfer literal coefficients without independent basis; Ehrhart/valuation extensions require their own assumptions. ## 6. Progressive loading — activation semantics are part of the algorithm Load only on material triggers: - explore/rigor -> `references/exploration_and_adaptive_rigor.md` - Pick theorem/roles -> `references/pick_abstraction.md`, `references/pick_representation.md` - architecture/provenance -> `references/theorem_provenance.md` - merge/continuation/channel equivalence or `MINIMAL` -> `references/decision_quotients.md` - audit/coverage -> `references/audit_and_contrast.md`, `references/review_scope_and_coverage.md`; software DELTA/FULL -> `references/software_audit_adapter.md` - audit near-miss/residual -> `references/audit_search_policy.md` - canonicalization seam -> `references/canonicalization_seam.md` - partial commit -> `references/partial_commit.md` - interaction-heavy audit -> `references/interaction_contrasts.md` - derivation/failure -> `references/procedure_gaps.md`, `references/binding_and_rebinding.md`, `references/execution_and_failures.md` - architecture/resolution -> `references/architecture.md`, `integration/procedure_resolution.md` - seam/history/time -> `references/seams_information_and_time.md` - probability/measure -> `references/probability_semantics.md` - composition/observation-value/refinement -> `references/composition_and_refinement.md` - null-conditioning/symmetry/Ehrhart/local-global gate -> `integration/specialized_gates.md` - prompt/presentation -> `references/prompt_and_presentation.md` - robustness -> `references/robustness.md` - output/calibration -> `templates/`, `examples/` Triggers are algorithmic. If required detail is unavailable, narrow or downgrade the conclusion rather than pretending it was applied.