Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dkernel Cert Cz Chunk15 Bri

The bridge theorem

In a large machine-checked proof, one of the most tedious jobs is making sure that two separately constructed objects really are the same. The declaration czChunk15_bridge is a formal theorem in the Recognition Science framework's machine-checked library of formal theorems. It states that a list called couplingChunk15, after being converted by a function named toCZ, equals the list czChunk15. The proof is by decide, meaning the computer checks the equality by direct computation over the finite list, with no symbolic reasoning steps.

The context is a verification effort for a four-dimensional identity in gravity analysis, specifically an identity about the midpoint m² TT (transverse-traceless) sector. The work is split into 16 chunks, numbered 0 through 15. Each chunk is a list of entries of a structure type called CZ, which packages integer coefficients for a gravity coupling term. The bridge theorems, one per chunk, connect the chunk lists to a separate list of coupling data. The theorem for chunk 15 is the last of these bridges, and its role is purely mechanical: it certifies that the two representations agree exactly.

What this theorem does not claim is any physics. It does not assert that the gravity identity itself is true, nor that the coupling data represent anything measured in an experiment. It only establishes a formal equality between two finite lists of integers. The theorem is a piece of bookkeeping, a certificate that a conversion step in a larger formal development was carried out correctly. Its value is in the audit trail: anyone who wants to trust the larger proof can check this bridge and know that this particular seam in the construction is sound.

In Recognition Science, this kind of certificate is part of the framework's discipline of exact provenance. The framework derives physical structure from a small set of axioms, and every step in that derivation is meant to be checkable. A bridge theorem like this one is a small but necessary rivet in that structure. It does not advance the physics; it secures the foundation on which the physics rests. For a reader, the practical consequence is confidence: the formal library has verified that this particular conversion is correct, so the larger argument can proceed without a hidden mismatch.

theorem czChunk15_bridge :
    couplingChunk15.toList.map toCZ = czChunk15 := by
  decide

theorem czChunk15_bridge :
    couplingChunk15.toList.map toCZ = czChunk15 := by
  decide

theorem czChunk15_bridge :
    couplingChunk15.toList.map toCZ = czChunk15 := by
  decide

What this page does not claim

The theorem does not assert the truth of any physical gravity identity. The theorem does not claim the coupling data represent measured experimental values. The theorem does not establish any property of the lists beyond their equality after conversion.

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/ReggeExactMidpointM2TTIdentity4DKernelCert.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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