Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dkernel Cert Cz Chunk14 Bri

The bridge theorem

A bridge theorem in a machine-checked library of formal theorems is a statement that two different descriptions of the same object agree. The declaration czChunk14_bridge is one such statement. It says that a list of coupling coefficients, written in one form, becomes exactly the same as a separate list of coefficients when converted through a small translation function. The proof is by decide, meaning the computer checks every entry by direct computation rather than by a longer chain of reasoning.

This particular bridge belongs to a larger verification effort. The library is checking an identity in four-dimensional gravity, called the midpoint m² TT identity, that involves a large table of integer coefficients. The table is split into sixteen chunks, numbered from zero to fifteen. Each chunk has its own bridge theorem, and czChunk14_bridge covers the chunk with index fourteen. The theorem states that the coupling list for that chunk, after mapping through the conversion function toCZ, equals the stored chunk list. The computation uses integer lists with scale-32 tables and a kernel-level decision procedure, without relying on native code execution.

What the theorem does not claim is just as important as what it proves. It does not say that the midpoint m² TT identity itself is true. It only says that two representations of one chunk of the coefficient table agree. The full identity, which would relate the explicit form of the tensor to the closed form, is a separate statement with its own proof obligation. The bridge also does not claim anything about the physical meaning of the coefficients, about why this identity should hold, or about any connection to the broader forcing chain of Recognition Science. Those are outside the scope of this declaration.

In practical terms, the bridge theorem is a consistency check. It confirms that the hand-written chunk list and the computed coupling list, for this one slice of the table, are the same object. That matters because a large verification proof is only as trustworthy as its smallest pieces. If every chunk passes its bridge check, the table is internally coherent. The theorem does not make the gravity identity true; it makes the table reliable enough to test the identity against.

theorem czChunk14_bridge :
    couplingChunk14.toList.map toCZ = czChunk14 := by
  decide

theorem czChunk14_bridge :
    couplingChunk14.toList.map toCZ = czChunk14 := by
  decide

What this page does not claim

The midpoint m² TT identity itself is not proved by this bridge theorem. No physical interpretation of the coupling coefficients is given here. This declaration does not connect to the broader forcing chain of Recognition Science.

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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