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Published July 16, 2026 | Version v11.0.0

Occurrence-Exact Paid Recomposition

Authors/Creators

  • 1. Independent Researcher

Description

v11.0.0 — Occurrence-Exact Paid Recomposition — promotes a Mathlib-free Witnessed theorem family for ordered payments and exact catalog adequacy. Ordered payments carry proof-relevant, occurrence-indexed removal equations and an exact computed residue; the total checker returns either such a trace or a scoped refusal and accepts exactly when a trace exists. Under exact attempt-level catalog completeness, paid global plans and paid catalog plans are equivalent without replacing native dependent receipts, expected-payment evidence, payment traces, or residue. A separate authorized/forged countermodel proves that endpoint-only completeness is insufficient. A public-only resource-trace application retains a resident checker receipt through the catalog conversions; a finite-support one-crossing application remains annex evidence because it imports a SCRATCH checker. The stable root imports only Payment and Catalog, and the evidence modules remain outside it. Acceptance of one submitted attempt, refusal in one named catalog, and global nonexistence under ExactPaidCatalogComplete are distinct scopes. This release claims no new cut connective or proof calculus, no Hall, matching, 3DM, CSP, or complexity novelty, no general plan synthesis, no persistent token serial, and no refusal transition, refusal debt-preservation, dynamic authority, resource creation, or temporal debt. ResourceCheckerExec.checkTrace = none means only rejection of that submitted trace; PC-1 and PC-2 remain closed, and stateful bounded realization/refusal remains outside v11. Full release history is in CHANGELOG.md; the v11 inventory and gates are in docs/V11-READINESS-LEDGER.md. The stable frame: the Lean work did not produce a unified calculus. It produced a set of small admissibility kernels, each isolating a different refusal boundary. The stack exposes a typed-verdict algebra (basis × precedence × standing) over partitioned governance state, with a typed pipeline from claim derivation through authorized execution, plus refusal-gate kernels for metric-time freshness, collapsed-surface authorization, witness invariance, and corrective monotonicity. General composition rules and meta-theorems are out of scope for 1.0 and remain separate kernel families. The 1.0 public surface comprises eight modules aggregated via AdmissibilityKernels.lean and is demonstrated by seven specimen consumers in Examples.lean. The artifact models when evidence-backed claims may authorize transitions, proves that boundary-crossing upgrades are impossible by construction, and refuses laundering across the surface, freshness, witness, and authority axes. Not a sequent calculus, not a process calculus, not a proof-theoretic admissibility logic, not a unified maximal calculus — see the repository's scope fence for the full list of non-claims. Annex modules build green and are available but are not part of the 1.0 compatibility claim. (Renamed 2026-06-03 from "Admissibility Calculus 1.0"; a deprecated compatibility shim at LeanProofs/Admissibility/CalculusOne.lean preserved the old import path through v9 and was removed in v10.0.0 — see the aggregator's migration note.) (v1.2 adds fenced UNRATIFIED-CANDIDATE No-Free-Lift candidate annexes and an experimental attestation-boundary wiring tree under experiments/, shipped with module names de-placarded and a composition-classification target naming the gate toward any future calculus claim; the 1.0 public surface and its non-claims are unchanged.) (1.4.0 promotes the ratified Witnessed Derivation Calculus — a narrow proof-theoretic calculus for witnessed movement across typed boundaries (composition, multi-context cut, soundness, provenance, non-manufacture, model-scoped normalization) — into the canonical public surface as the Mathlib-free LeanProofs.Witnessed.* library, with a build-graph-enforced no-Mathlib boundary and an axiom-footprint regression gate. It is additive: the 1.x Admissibility surface is unchanged, and it is not a revival of the retired maximal "Admissibility Calculus".) (3.0.0 completes the bounded lifecycle-calculi family: nine ANNEX release-surface calculi — temporal custody, surface projection, refusal/denial, boundary artifacts, obligation/residue, safety preservation, execution custody, boot/genesis, checkpoint settlement — with no master Admissible judgment; the aggregate import proves checkability only.) (4.0.0 adds the Custody-Indexed Sequents campaign: a parameterized indexed-sequent skeleton, fenced under Scratch and CI-covered as its own build target, where structural read discipline is explicit, contraction is priced across Cartesian and linear instances, bridge composition preserves provenance, index connectivity does not imply derivability, master shapes are screened on both faces — universal indices and universal evidence — and derived evidence cannot become universal bridge currency: every cross-index derivation roots in read evidence whose original scope funded it. The 1.0-era "not a sequent calculus" non-claim was scoped to the stable kernel surface and remains true of it; v4's sequent discipline is a distinct, fenced object beside it, and full Gentzen cut elimination is explicitly NOT claimed — custody-preserving normalization is the named v5 target.) (5.0.0 delivers that target: normalization is partial and policy-aware — a liberal structural derivation normalizes into the custody discipline iff its reads can be paid by occurrences, per-label counting decides normalization exactly, refusal is a typed forgery whose named offender genuinely exceeds supply, successful normalization conserves occurrences for every measure and preserves the custody chain, and a positional occurrence trace proves which occurrence paid which read — no occurrence pays twice, nothing pays that was not there. Not full Gentzen cut elimination; not runtime; scoped to the liberal/linear normalization skeleton over the v4 sequent systems.)

Notes

If you use this software, please cite it as below.

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Related works

Is supplement to
Software: https://github.com/unpingable/lean/tree/v11.0.0 (URL)

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