Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dkernel Cert Cz Chunk13 Bri

The bridge theorem

In formal verification, a large computation is often split into pieces so that each piece can be checked by a computer. The declaration czChunk13_bridge is one such piece. It states that two lists of records, one called couplingChunk13 and the other called czChunk13, are identical after a conversion step. The conversion, named toCZ, maps one representation of the data into another. The theorem proves that the mapped version of the first list equals the second list, and the proof is carried out by the kernel's decide tactic, meaning the computer checked the equality by direct computation.

The context for this theorem is a larger effort to verify an identity about gravity in four dimensions. The identity involves a quantity called m² and is checked at a midpoint. The verification is split into sixteen chunks, numbered from zero to fifteen. Each chunk is a list of records of type CZ, which is a structure holding integer values. The bridge theorems, one for each chunk, connect the chunk lists to corresponding coupling lists. The declaration czChunk13_bridge is the bridge for chunk thirteen. Together with the other bridges, it ensures that the data used in the verification is consistent across the two representations.

The theorem does not, by itself, prove the gravity identity. It only establishes that the two tables for chunk thirteen agree. The actual identity is the subject of other declarations in the same file, such as symFullZ_explicit_eq_closed, which states that two different formulations of a symmetry condition are equal. The bridge theorem is a supporting step, not the main result. It is also not a statement about physics directly; it is a statement about data structures and their equality. The value of the theorem is that it closes a gap in the chain of evidence, making the overall verification more trustworthy.

What the declaration does not claim is equally important. It does not claim that the gravity identity is true, nor does it claim that the chunk lists are correct in any physical sense. It only claims that the two lists agree after conversion. It also does not claim anything about the other chunks; each bridge theorem is separate. A reader who wants to know whether the full identity holds must look at the other theorems in the file. The bridge theorem is a piece of the puzzle, not the whole picture.

theorem czChunk13_bridge :
    couplingChunk13.toList.map toCZ = czChunk13 := by
  decide

theorem czChunk13_bridge :
    couplingChunk13.toList.map toCZ = czChunk13 := by
  decide

theorem czChunk0_bridge :
    couplingChunk0.toList.map toCZ = czChunk0 := by
  decide

What this page does not claim

The theorem does not prove the gravity identity itself. The theorem does not assert that the data in the lists is physically correct. The theorem does not cover the other fifteen chunks.

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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: