lean

What this is

This is a Lean 4 proof workbench for governed computation: formal models of when evidence licenses a conclusion or state transition, and when standing, custody, authority, spend, history, refusal, or obligation remains an independent condition.

It does not primarily formalize proofs about proofs or the act of formalization. It formalizes the admissibility of consequential judgments and transitions. Proof-producing checkers and evidence data are governed objects inside that subject, not the subject’s replacement.

The central question is not merely “can the machine take this transition?” It is:

What exact evidence justifies this judgment, at these indices, under this actor’s standing and custody—and what remains unresolved afterward?

That question is useful in authority-bearing, externally consequential systems. A reachable endpoint can have an unlawful history. Custody can exist without authority. Standing can coexist with refusal. A successful and safe effect can leave an obligation undisclosed or undischarged. In the modules that store native decisions, replaying their projections preserves the stored result without earning a fresh receipt.

Most modules follow a small formal-methods pattern:

  1. state a bounded judgment or transition model;
  2. identify the evidence and indices that support it;
  3. make the tempting stronger inference explicit; and
  4. prove the permitted bridge or exhibit a countermodel to the invalid one.

The unusual words name different mathematical objects. A Witness is evidence indexed by a particular claim. A Refusal is structured evidence for non-admission, not a bare Boolean. Standing concerns the claim’s basis; Custody concerns provenance intactness; Spend is family-native resource consumption; and Obligation concerns what remains live after action. A hostile countermodel is deliberately qualified against a tempting semantic lift: it retains plausible neighboring premises while refuting the stronger conclusion. The semantic guardrail table records the exact orientation and prohibited reductions.

The public calculi

The repository contains several independently scoped formal families. The v14 Governed Admissibility Calculus supplies claim-indexed witness/refusal data, separate standing/custody/obligation books, bounded instances, exact refusal encodings, stored decisions, and an origin/history-sensitive BreakGlass instance.

V15 adds a Cross-Calculus Atlas over selected edges from Governed Transport, Execution Custody, and Continuity Admission. The mappings preserve the native indices and exact receipts required by those edges. They do not identify the three calculi, translate every theorem, or create a shared algebra. StaticRole is a held-out partial instance closed at R3; Inquiry and Preparation remain independent comparison-only neighbors.

V16 adds Governed Transition Boundaries, a separate public-evidence surface asking one orthogonal question: for a selected target and a selected view of the source, is there a single total decoder recovering the target from the view, correctly for every source? Four axiom-free results establish that such explicit factorizations compose, that they imply the public ViewSemantics.Determines fibre-constancy relation, that a target-distinguishing collision blocks them, and that deterministic postprocessing of an insufficient view does not restore them. The converse is not claimed. One declared finite language carries a unique least target-determining selection, and five witnesses — fixed-policy authorization refusal, selected-context validation, bounded capacity realizability, occurrence-link observation, and modeled hidden-relation nonidentifiability — are each bounded to their own fixture. The generic statements are standard function-factorization and view-determinacy facts and the finite result is an exhaustive dependency calculation; the contribution is their mechanically checked synthesis, and no novelty or priority is claimed. V16 promotes no stable surface and the V15 ATLAS classification is unchanged.

Governed Transport is not defined as a morphism. Its Span is only bare proof-relevant crossing geometry; certificate-dependent lift, translation, and target-local reliance are separate types, and the span itself supplies no authority law. A categorical model could describe some structure only after these governed distinctions and their omissions are kept explicit.

The bounded BreakGlass instance is likewise not an axiom. It constructs an exceptional permit and origin-bound attempt, commit, execution receipt, obligation, audit record, and settlement lifecycle. Exceptional authority does not silently become ordinary authorization or clean history.

What this is not

This is not a blockchain or cryptocurrency protocol, zero-knowledge system, legal-evidence product or legal protocol, smart-contract framework, generic audit-log implementation, category-theory library, generic state-machine verification project, or alternate-reality game. Nor is it a relabeling of ordinary proof theory or programming-languages metatheory. Those areas may instantiate or orient some formal structures in the repository, but none supplies its definition or intended classification. The public records are ordinary source and verification receipts, not an interactive reveal.

It is also not a universal theory of institutions, a complete model of machine judgment, a JCP implementation, an operational AG/NQ realization, or a claim that every governed process reduces to one calculus.

Formal result versus deployed system

Lean checks the theorems under their disclosed definitions, hypotheses, and axiom footprints. It does not prove that a runtime implements them. A runtime conformance claim requires a separately scoped correspondence map, executable preservation evidence, and revision-bound qualification receipts for every governed distinction.

For the first technical orientation and an end-to-end example, read the plain-language summary. For exact theorem scope, read WHAT-THIS-PROVES.md. The source and build commands are in the README.