Gravity Track1 Bcompiler Trust Status Track1 Bcompiler Trust Status Anchors Clos

Compiler trust at the gate

A ledger is a discrete record of events, and the Recognition Science framework keeps one for its own proofs. This declaration is a page in that ledger. It records, in a machine-checkable structure, that a particular proof about a quadratic gate at the value N = 5 was closed using a compiler's native computation, and that doing so extended the kernel basis beyond the standard three axioms.

The standard basis for the framework's machine-checked library of formal theorems is exactly three axioms: propositional extensionality, classical choice, and quotient soundness. The declaration states that the proof of the corrected Track 1.B gate at N = 5 relies on native_decide, a mechanism that lets the kernel trust the compiler's reduction of boolean expressions. This introduces two extra axioms: Lean.ofReduceBool, which allows that trust for boolean reduction, and Lean.trustCompiler, which grants general compiler trust for native computation.

The anchoring theorem, track1BCompilerTrustStatus_anchors_closed_gate, establishes two facts together. First, that the trust status record correctly says the proof uses native_decide. Second, that the gate itself is closed, meaning gate_open = false in the corrected status. The gate is closed at N = 5, but the all-cardinality generalization, the statement that the gate closes for every possible value, remains open. The declaration does not claim that generalization.

What this changes is the epistemic weight of the gate result. A reader can see, from the record alone, that the proof is not axiom-clean in the standard sense; it leans on compiler trust. That is a real distinction in the framework's accounting, where the standard basis is audited to exactly three axioms. The declaration makes the cost of the proof visible, and it leaves the broader question of whether the gate holds for all cardinalities as a target, not a result.

/-- The compiler-trust status of the Track 1.B corrected gate at `N = 5`.
The gate is closed via `native_decide` (see
`Track1BCorrectedQuadratic.correctedTrack1BGateAtN5_closed`), so the kernel
basis is extended by `Lean.ofReduceBool` and `Lean.trustCompiler` on top of
the standard `propext / Classical.choice / Quot.sound` basis. The
all-cardinality generalization remains open. -/
def track1BCompilerTrustStatus : CompilerTrustStatus where
  uses_native_decide := true
  extra_axioms := ["Lean.ofReduceBool", "Lean.trustCompiler"]
  standard_basis := ["propext", "Classical.choice", "Quot.sound"]
  all_cardinality_open := true

/-- The compiler-trust status of the Track 1.B corrected gate at `N = 5`.
The gate is closed via `native_decide` (see
`Track1BCorrectedQuadratic.correctedTrack1BGateAtN5_closed`), so the kernel
basis is extended by `Lean.ofReduceBool` and `Lean.trustCompiler` on top of
the standard `propext / Classical.choice / Quot.sound` basis. The
all-cardinality generalization remains open. -/
def track1BCompilerTrustStatus : CompilerTrustStatus where
  uses_native_decide := true
  extra_axioms := ["Lean.ofReduceBool", "Lean.trustCompiler"]
  standard_basis := ["propext", "Classical.choice", "Quot.sound"]
  all_cardinality_open := true

/-- **Anchoring theorem.** The trust-status record is anchored to the real
result: the corrected Track 1.B gate at `N = 5` is closed
(`gate_open = false` in `correctedTrack1BStatus`), discharged by
`native_decide` via `correctedTrack1BGateAtN5_closed`, and the trust status
correctly records `uses_native_decide = true`. -/
theorem track1BCompilerTrustStatus_anchors_closed_gate :
    track1BCompilerTrustStatus.uses_native_decide = true ∧
    Track1BCorrectedQuadratic.correctedTrack1BStatus.gate_open = false := by
  exact ⟨rfl, rfl⟩

What this page does not claim

The declaration does not prove that the gate holds for all cardinalities. It does not claim that the proof is axiom-clean in the standard sense. It does not assert that compiler trust is unsound, only that it is an extension.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Gravity/Track1BCompilerTrustStatus.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: