Gravity Track1 Bcompiler Trust Status

Compiler trust and the closed gate

A proof in a formal library is only as strong as the assumptions it leans on. Most proofs in the Recognition Science library rest on three standard axioms of the underlying logic: propositional extensionality (two propositions are equal when they imply each other), choice (from every nonempty set you can pick an element), and quotient soundness (identifying equivalent elements is consistent). These three form the standard basis. A proof that uses only them is axiom-clean in the strongest sense.

The Track 1.B corrected gate at N = 5 is not such a proof. Its verification uses a mechanism called native_decide, which lets the kernel trust the compiler's own reduction of boolean expressions. That trust is recorded as two extra axioms beyond the standard three: Lean.ofReduceBool and Lean.trustCompiler. The module CompilerTrustStatus is a machine-checkable structure that stores exactly this information: whether the proof used native_decide, which extra axioms it introduced, what the standard basis is, and whether the all-cardinality generalization is still open.

What does this mean in plain language? The gate at N = 5 is closed: the record track1BCompilerTrustStatus_anchors_closed_gate confirms that gate_open = false. But the proof of that closure leans on the compiler, not only on the three standard axioms. The framework is being honest about this. It does not pretend the gate is axiom-clean when it is not. Instead, it records the exact extension to the basis, so anyone reading the result knows precisely what was assumed.

The all-cardinality generalization, the statement that the gate closes for every N, remains open. The module flags this with all_cardinality_open = true. That is a target, not a failure. The framework's library treats an open problem as a named goal, and this record is the ledger entry that names it.

/-- **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⟩

/-- 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

What this page does not claim

This module does not claim that the N = 5 gate is proved without compiler trust. This module does not claim that the all-cardinality generalization is proved or even attempted. This module does not describe what physical meaning the Track 1.B gate has in the gravity theory.

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

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