Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk07 E 130013

A numerical identity in a gravity computation

In numerical analysis and physics, a computation often reduces to checking that two different-looking expressions produce the same number. The declaration e_130013 is one such check. It states a specific equality: for a particular choice of six indices, the value of a function called m2Num equals eight times the value of a function called explicitZ. The proof is not a long argument; the Lean code closes the statement with by decide, meaning the computer simply evaluates both sides and confirms they match.

The names carry the context. The functions belong to a module about gravity analysis, specifically a family of identities called the M2 TT identity in four dimensions. The index pattern 1 3 0 0 1 3 identifies one point in a large grid of cases. The factor of eight is not accidental; it is the same factor that appears throughout the chunk, which covers 256 such cases. The docstring for the chunk says it is the seventh of several pieces and that it decides those 256 cases. The theorem e_130013 is one entry in that list, a single verified row in a table of arithmetic identities.

In Recognition Science, this theorem is part of a machine-checked library of formal theorems. The library does not merely assert the identity; it records a proof that a computer has verified step by step. That makes the claim about the arithmetic exact, within the formal system's rules. The practical meaning is narrow but solid: for this index choice, the two expressions agree, and the agreement is not approximate or fitted but exact.

What the declaration does not claim is equally clear. It does not say anything about the physical meaning of m2Num or explicitZ, about whether the larger M2 TT identity holds for all indices, or about whether the gravity analysis itself is correct. It is a local, computational fact. A reader should not infer from this single theorem that the whole identity is proven, nor that the framework has derived any property of gravity from it. The theorem is a brick, not the building.

theorem e_133333 : m2Num 1 3 3 3 3 3 = 8 * explicitZ 1 3 3 3 3 3 := by decide

theorem e_133333 : m2Num 1 3 3 3 3 3 = 8 * explicitZ 1 3 3 3 3 3 := by decide

What this page does not claim

The theorem does not prove the entire M2 TT identity for all index choices. The theorem does not establish any physical property of gravity. The theorem does not assign physical meaning to the functions m2Num or explicitZ.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk07.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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