lean

V16 — Governed Transition Boundaries

Start here. Release orientation: what shipped, what it does and does not establish, and how to verify it.

Status: released 2026-07-28.

Subtitle: Which selected targets factor through which source views.

v16 adds one public-evidence surface. It asks a single question in a mechanically checked form: given a target and a view of the source, is there one total decoder that recovers the target from the view, correctly for every source? Four generic theorems answer the structural half, and one declared-finite calculation plus five bounded witnesses answer instances of it.

The version DOI is minted by the GitHub release creation and recorded from Zenodo afterward, never guessed here. The concept DOI 10.5281/zenodo.20369489 identifies the series and does not move.

What is proved

Generic core (LeanProofs.GovernedTransitionBoundaries, four axiom-free receipts). ExplicitlyFactorsThrough view target holds when one total decoder is correct for every source. Such factorizations compose; they imply the existing public ViewSemantics.Determines fibre-constancy relation; a target-distinguishing collision blocks them; and a carrier obtained solely by deterministic postprocessing of an insufficient view does not restore them.

The converse is not proved and is not true in general: for arbitrary types, fibre constancy does not construct representatives of reachable view fibres or values for unreachable view outputs. Quotient and coequalizer settings, and a surjective view with a section, are positive controls only when that additional lifting data is actually present.

Declared finite representation (…Evidence/FiniteRepresentation.lean). In a declared seven-coordinate language, with a declared source list of length 1,024 covering every AnalysisCase and 128 duplicate-free coordinate selections: internalMinimum is the unique least selection determining the selected five-component target in the declared AtlasSelection.Includes order; exactly two masks in the enumeration determine that target, with membership, count, and duplicate freedom proved; the declared six-field carrier explicitly factors the five-target result; and no declared selection factors the modeled hidden relation or the combined six-target result.

This is functional dependency in a fixed table and a fixed coordinate language. It is not statistical sufficiency, arbitrary-carrier minimality, or a canonical global semantics.

Five bounded witnesses. Each is scoped to its own fixture and claims nothing beyond it.

Witness What it shows What it is not
Fixed-policy authorization refusal One product computes its target while one fixed grant-list policy refuses inspection and reliance A general authorization theory
Selected-context validation One issued observation record does not factor the validation target across two use contexts A temporal, expiration, revocation, or certificate-lifecycle result
Bounded capacity realizability Per-pair support records revalidate at the empty prefix while the three-event execution type is uninhabited General amalgamation, CSP consistency, or schedulability
Occurrence-link observation Two worlds share a present-state view and differ on one occurrence-link Boolean Causality, proof of occurrence, or a hyperproperty
Modeled hidden-relation nonidentifiability Two worlds agree at the admitted acquisition interface and differ on one hidden Boolean Physical truth, attestation correctness, or causal identification

The constructors in the context-validation fixture carry no temporal or prefix order. “Transition-relative computation” is a bounded program label for the observation that some targets factor through views carrying transition or history context when they do not factor through a coarser projection; it defines no operational semantics.

What is not new

The generic statements are standard function-factorization and view-determinacy facts, and the finite result is an exhaustive functional-dependency and attribute-selection calculation. The contribution is their mechanically checked synthesis with the five separately scoped witnesses. No novelty or priority is claimed. The nearest established structures are named in the public index, with the closest being the database distinction between view determinacy and rewriting.

Relation to v15

v15 is a Cross-Calculus Atlas of selected, receipt-indexed correspondences that preserves native indices and receipts without selecting a shared bridge algebra. Its ATLAS classification and its four negative results — FRONTIER-NOT-COMPOSITIONAL, NO-USEFUL-OWNERSHIP-COMMONALITY, CONTEXT-TRANSPORT-NOT-GENERIC, ONLY-DOMAIN-SPECIFIC-RESIDUAL-THEORIES — are unchanged and remain authoritative.

v16 asks a different question: which selected targets uniformly factor through which views. It neither replaces the v15 bridge surfaces nor promotes a shared cross-calculus semantics. No existing public module depends on it; its core and evidence are separately rooted.

Custody position

v16 promotes no stable surface. The ten new sources are PUBLIC-EVIDENCE under two new registered targets; scripts/stable-surfaces.tsv and every registered stable root’s import list are unchanged from v15. The sources are byte-pinned: the crossing gate reproduces each public SHA-256 and Git blob and re-derives the extracted body by removing exactly the twelve-line custody block.

  v16 v15
public Lean sources 283 273
stable / evidence / aggregate 115 / 167 / 1 115 / 157 / 1
stable roots / ownerships 12 / 142 12 / 142
registered targets 30 28
new receipts 29

Verification

The repository pins Lean 4.29.0 (leanprover/lean4:v4.29.0). Pass/fail is the exit code of the bare command.

lake build GovernedTransitionBoundaries GovernedTransitionBoundariesEvidence
bash scripts/check-governed-transition-boundaries-crossing.sh
bash scripts/check-governed-transition-boundaries-footprint.sh

The footprint gate replays all 29 receipts: 16 axiom-free, 7 [propext], 6 [propext, Quot.sound], zero Classical.choice, zero sorryAx. The full battery and per-gate results are in V16-READINESS-LEDGER.md.

Ordered from orientation to exact accounting. Stop wherever your question is answered.

  1. This document — what shipped and why.
  2. V16-GOVERNED-TRANSITION-BOUNDARIES.md — exact per-witness fences and the reference list.
  3. V16-PUBLIC-INDEX.md — module map, prior-art anchors, and the complete non-claim ledger.
  4. V16-RELEASE-LEDGER.md — release identity and frozen accounting.
  5. V16-READINESS-LEDGER.md — source pins, axiom accounting, and the qualification commands.

Reference: V16-PUBLIC-SOURCE-CROSSING-RECEIPT_2026-07-26.md — per-file digest table, frozen at the pre-release state.