Gravity Analysis Regge Ttalgebraic Closer Raw Cosine Support Eq Raw Moment Suppo

The bridge equality

In the Recognition Science framework's machine-checked library of formal theorems, the declaration rawCosineSupport_eq_rawMomentSupport proves that two tables of numbers are identical. The first table, called the cosine support, comes from a derivation on a periodic geometric grid. The second, called the moment support, comes from a literal transcription of the same geometric objects. The theorem states, in the framework's own terms, that these two tables are equal.

The equality matters because it bridges two ways of building the same object. One side is derived through a chain of definitions on a Freudenthal cube triangulation, a standard way to subdivide a cube into tetrahedra. The other side is a core table that was independently grounded against the same geometry. The theorem confirms, case by case, that the derived table and the transcribed table agree. This is a genuine cross-check, not a comparison of a source with itself.

The proof is a finite algebraic identity. It unfolds the two definitions and rewrites one table key into the other using a smaller lemma about slot midpoints. That lemma itself is proved by checking all 216 cases with the kernel's case analysis. The whole proof uses no axioms beyond the standard trio of the ambient type theory, and it contains no sorry or admit.

What the declaration does not claim is just as important. It does not say anything about the physical meaning of the tables, about gravity, or about the continuum limit. It only says that two finite tables of numbers are equal. It does not claim that the derivation is correct in any physical sense, only that it agrees with the transcription. It also does not claim that the tables are valid at aliased side lengths; the equality holds only at non-aliased sizes, and the framework explicitly discloses that no repair is attempted at the aliased ones.

/-- The production cosine support is the bridge moment support. -/
theorem rawCosineSupport_eq_rawMomentSupport :
    ReggeTTBlochAssembly.rawCosineSupport =
      ReggeTTGateBBridge.rawMomentSupport := by
  unfold ReggeTTBlochAssembly.rawCosineSupport
    ReggeTTGateBBridge.rawMomentSupport
  rw [bucketKeyOf_eq]

/-- The production cosine support is the bridge moment support. -/
theorem rawCosineSupport_eq_rawMomentSupport :
    ReggeTTBlochAssembly.rawCosineSupport =
      ReggeTTGateBBridge.rawMomentSupport := by
  unfold ReggeTTBlochAssembly.rawCosineSupport
    ReggeTTGateBBridge.rawMomentSupport
  rw [bucketKeyOf_eq]

/-- The production cosine support is the bridge moment support. -/
theorem rawCosineSupport_eq_rawMomentSupport :
    ReggeTTBlochAssembly.rawCosineSupport =
      ReggeTTGateBBridge.rawMomentSupport := by
  unfold ReggeTTBlochAssembly.rawCosineSupport
    ReggeTTGateBBridge.rawMomentSupport
  rw [bucketKeyOf_eq]

What this page does not claim

The declaration does not claim any physical meaning for the tables. It does not claim validity at aliased side lengths. It does not claim that the derivation is physically correct, only that it agrees with the transcription.

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/Analysis/ReggeTTAlgebraicCloser.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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