Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dkernel Cert Cz Chunk12 Bri

The bridge theorem

A bridge theorem in a machine-checked library of formal theorems is a proof that two separately defined objects are actually the same object. The declaration czChunk12_bridge proves that couplingChunk12.toList.map toCZ = czChunk12, meaning the twelfth chunk of coupling data, after being converted by the function toCZ, is identical to the twelfth precomputed chunk of kernel certificates. The proof is by decide, which means the machine checked every case directly and found no counterexample.

This is a bookkeeping fact, not a physics result. The theorem does not say anything about gravity, about the midpoint m² TT identity, or about the meaning of the chunks. It only says that two lists of numbers, one produced by a coupling calculation and one stored as a certificate, agree exactly. The certificate chunks are part of a larger verification structure: the docstring describes them as kernel certificates for the midpoint m² TT identity, generated by a script using integer list folding and scale-32 tables, with the kernel's decide tactic as the only verification method.

The practical value is trust in scale. The full calculation spans sixteen chunks, from czChunk0 to czChunk15, each with its own bridge theorem. A human checking every entry would be slow and error-prone; the machine checks all of them in one pass. The theorem czChunk12_bridge is one of sixteen such checks, and together they confirm that the coupling data and the certificate data tell the same story at every position.

What the theorem does not claim is just as important. It does not claim that the midpoint m² TT identity itself is true, that the coupling calculation is physically correct, or that the certificates are the right ones. It only claims that two specific lists of numbers are equal. The physics, the derivation, and the choice of certificates all live outside this theorem. The bridge is a check of internal consistency, not a proof of external truth.

theorem czChunk12_bridge :
    couplingChunk12.toList.map toCZ = czChunk12 := by
  decide

theorem czChunk12_bridge :
    couplingChunk12.toList.map toCZ = czChunk12 := by
  decide

What this page does not claim

The theorem does not prove that the midpoint m² TT identity itself is true. The theorem does not establish any physical claim about gravity or about the correctness of the coupling calculation. The theorem does not say that the certificates are the right ones, only that two lists of numbers agree.

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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