lean

V15 presentation semantic audit — 2026-07-22

Scope and method

This is the second-pass audit of the reader-facing orientation added after the operator-ratified V15 candidate. The audit treats familiar formal-methods vocabulary as an entry point only when it does not replace a native judgment. It covers README.md, WHAT-THIS-IS.md, WHAT-THIS-PROVES.md, CHANGELOG.md, CITATION.cff, the V15 public index, release-candidate and readiness pages, the plain-language summary, and the calculus landing page.

The lexical pass searched every occurrence of morphism, categorical, adjunction, cryptographic, commitment, derivation tree, axiom, blockchain, smart contract, chain of custody, proof about proofs, state machine, capability, effect, proof object, derivation, trace, certificate, authorization token, and audit log. Historical release descriptions were checked in place and retained when they name an actual type, theorem, audit class, or then-current result.

Correction ledger

Risky translation found Why it was misleading Replacement Lean anchor
Receipts were summarized as though every one bound source, target, subject, context, and route. No single repository-wide receipt record has all of those fields. PJ supplies a bridge-specific dependent family; GT and Execution Custody instantiate different evidence. The public pages now define a receipt as the exact semantic evidence type required by the rule in context, then describe each V15 instance separately. They explicitly deny inherent signature, hash-chain, zero-knowledge, or other cryptographic content. PJ.IndexedJudgmentBridge.Receipt, RouteReceipt, ExactStageReceipt
Stored origin and history were presented as a universal receipt behavior. Origin and stored-history coordinates occur only in calculi that define them. Replay and origin claims are now instance-qualified; the Admissibility crossing’s stored pair and the BreakGlass history rules are named directly. NativeDecisions, BreakGlass
Governed Transport could be read as a route-like morphism carrying proof data. Span deliberately has no preservation or authority law. Candidate/certificate lift, translation, and target-local reliance are separate structures, and GT does not grow custody, spend, or obligation fields by analogy. GT is now introduced as crossing geometry plus separately supplied lift, translation, and reliance laws. A bare-morphism reduction is prohibited explicitly. Span, CandidateLift, CertificateLift, TranslateAlong, and RelyLocally
“Anti-minting” could be read as generic derivation reconstruction or universal unforgeability. The V15 theorem has a much narrower codomain and premise: it rules out ReceiptFreeMintAt at a source/target pair where NotEntitledFrom is known. The pages now name the exact prohibited mint: source-relative EntitledFrom from two bare inhabited judgments at the refused pair. They deny a generic result about evidence, standing, custody, spend, discharge, closure, history, origin, or cryptographic forgery. ReceiptFreeMintAt, exact_receipt_prevents_target_minting
BreakGlass appeared before an explicit non-axiom explanation. “Break glass” can sound like a logical escape hatch even though the implementation constructs ordinary Lean structures and a governed family. It is now described as an exceptional permit/attempt/commit/receipt/obligation/settlement lifecycle, with origin/history separation and refusal outside its envelope; the pages state directly that it is not an axiom. ExceptionalPermit, ExecutionReceipt, ReconciliationObligation, governedFamily
Hostile countermodels were called counterexamples without fully stating the qualification method. That wording did not explain why the examples are constructed to retain plausible premises while defeating one proposed lift. The public explanation now defines hostile construction as adversarial qualification and gives three named non-implication results. custody_does_not_grant_dynamic_authority, may_attempt_not_entitled_to_commit_without_local_preconditions, safety_does_not_supply_discharge_receipt
The top-level pages did not expressly exclude reflexive “formalization of formalization.” Evidence data and proof-producing checkers could cause a reader to mistake governed objects for the repository’s primary subject. The README, plain-language summary, and WHAT-THIS-IS.md now say that the subject is admissibility of consequential judgments and transitions, not primarily the act of formalization. GovernedFamily, ResourceChecker
Application exclusions lacked a positive boundary. A list of “not blockchain / not legal tech” still left the defining application class unclear. The orientation now separates the formal subject, possible instantiations, and non-exclusive examples. Documentation boundary; no production-system correspondence theorem is claimed.

Four-category terminology classification

The categories are: 1 exact theorem-backed characterization, 2 partial analogy, 3 implementation or application possibility, and 4 unsupported substitution.

Term or occurrence family Category Classification and disposition
Derivation, derivation trees, and positional traces in the WDC release history and technical reference 1 These name the actual Derivation, Checks, and ResourceCheckerExec.Trace objects. Historical and technical uses remain unchanged.
Trace, Certificate, and Commitment where capitalized type names or exact module families are named 1 DynamicTrace, CertificateLift, PolicyCertificate, BoundCertificate, CommitmentStanding, and AuditCommitment are repository identifiers. AuditCommitment is not thereby cryptographic.
axiom in footprint reports, the removed placeholder history, and the repository’s axiom-classified posture 1 These refer to Lean axiom dependencies, declarations, or audit classes. The new BreakGlass sentence uses the word only to deny that classification.
transition-system, state-machine, derivation, proof-object, capability, effect, trace, certificate, or audit-log comparisons in the new orientation 2 Retained only as marked comparisons or prohibited collapses. The native type is defined first, and the page states which governed coordinates the analogy omits.
categorical language and morphism 2 No categorical equivalence is claimed. The only new affirmative sentence says that a categorical model could describe some structure only while preserving the additional governed data; all other occurrences reject a morphism/equivalence collapse. No functor or adjunction result is advertised.
blockchain, legal evidence, enclaves, cryptographic protocols, deployment, incident response, and institutional workflow examples 3 Kept in the applications boundary as possible instantiations. None is named as the defining domain or as an implemented production correspondence.
receipt = cryptographic commitment, signature, hash chain, zero-knowledge proof, transaction receipt, or legal custody proof 4 Rejected. Current occurrences are explicit nonclaims. Repository hashes and release receipts remain artifact provenance, not properties of every semantic receipt.
governed transport = bare morphism 4 Rejected and replaced by the exact four-layer GT orientation.
anti-minting = recovery of an original derivation tree or generic cryptographic unforgeability 4 Rejected and replaced by the exact ReceiptFreeMintAt / EntitledFrom statement.
BreakGlass = exceptional axiom 4 Rejected and replaced by its explicit constructed lifecycle.
project = proof about proofs, generic state-machine verification, category theory, blockchain, legal protocol, or theatrical artifact 4 Rejected at the top level. Those comparisons no longer define the project.

No occurrence of adjunction or authorization token remains in the reviewed reader-facing surface. cryptographic commitment, chain-of-custody, proof object, and audit log occur only in explicit fences or analogy warnings. The long historical README and changelog retain exact names such as Witnessed Derivation Calculus and Dynamic Trace; rewriting those names would falsify the historical formal surface rather than improve orientation.

Retained analogies and their fences

Terms deliberately left unusual

Standing, Custody, Authority, Spend, Refusal, Obligation, Receipt, Hostile countermodel, Anti-minting, BreakGlass, and Atlas remain in the public vocabulary. Replacing them wholesale with role, possession, capability, error, postcondition, proof object, counterexample, unforgeability, exception, or equivalence would erase distinctions proved independent in the repository. The compact entry definitions and prohibited reductions are in the README semantic guardrails.

Applications boundary

The formal subject is governed admissibility of consequential judgments and transitions. Operational automation, deployment and promotion, administrative workflows, incident response, security authority boundaries, evidence-bearing inquiry, resource-consuming transitions, and distributed or institutional decisions are possible instantiations. Blockchain, legal evidence, enclaves, and cryptographic protocols are non-exclusive examples; none defines the project, and none contributes domain-specific guarantees without a separate formal model.

Validation receipt

The review began at commit 24e3c0dd9488804ba7432e90aabfae7630b2ca3e (tree 28ff282a4fb50a7d51bf05f82033c76f4391c7a4). The following commands were run against the edited worktree:

Command Result
lake build V15Integration PASS, 60 jobs
lake build V15IntegrationQualification PASS, 70 jobs
lake build PASS, 224 jobs
python3 scripts/check-v15-integration.py PASS; 4 PJ manifests, 1,950 cumulative declarations, 74 cumulative axiom-bearing entries, 1,005-declaration Continuity correspondence, source pins, Track A freeze, and ATLAS verdict preserved
python3 scripts/check-v15-public-qualification.py PASS; 2,606 declarations, 953 theorems, 735 hostile-module declarations, and 12 representative collapses
python3 scripts/check-v15-continuity-rename.py PASS; 1,005 declarations preserve type, value, and axiom identity
bash scripts/check-custody-classes.sh PASS; all 273 public Lean sources close exactly
bash scripts/check-mathlib-free-targets.sh PASS; 28 registered targets and 273/273 source ownership
bash scripts/audit-axioms.sh PASS; 23 signature, 0 interface-law, 8 specimen, 0 forbidden, 0 unclassified declarations
bash scripts/audit-native-decide.sh PASS; 6 allowed finite-witness occurrences
bash scripts/check-mathlib-pin.sh PASS; manifest and lakefile both pin 6ef8cc2731780be866bf243afcb7732f4da5f406
local Markdown target check over the eight edited/indexed reader documents PASS; 0 broken local links
python3 -m py_compile scripts/check-v15-public-qualification.py PASS
parse CITATION.cff and assert version/no release date PASS; 15.0.0, no date-released field
git diff --name-only -- '*.lean' PASS; empty
git diff --check PASS

Two historical commands are not gates in this tree: scripts/formalization_audit.py does not exist, and the old aggregate names CalculiStable CalculiScratch CalculiAll Calculi are not Lake targets. Their attempts therefore returned “file not found” and “unknown target,” respectively. The current registered-target gate above enumerates and checks the repository’s 28 public targets. No standalone Pages/Jekyll/MkDocs build is configured; GitHub Pages renders the repository README, whose local links were checked directly.

No Lean source, theorem statement, namespace, source-calculus pin, version, tag, or release state changed in this pass.