Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk08 E 200013

A numerical identity in the gravity analysis

The declaration e_200013 is one entry in a large table of machine-checked theorems. Each theorem states that a particular computed value, written m2Num with six index numbers, equals eight times another computed value, written explicitZ with the same six index numbers. The proof method is "by decide", which means the computer algebra system directly evaluates both sides and confirms they are equal. This is a brute-force arithmetic check, not a derivation from physical principles.

The table lives in a file whose name mentions Regge calculus, a numerical approach to general relativity that approximates spacetime by flat building blocks. The file also mentions "exact midpoint" and "TT identity", suggesting the values relate to a specific geometric configuration and a transverse-traceless condition. The declaration e_200013 itself, however, contains no physics. It only asserts the equality of two numbers for one specific set of six indices.

In the Recognition Science framework, this theorem is part of a larger verification effort. The framework's machine-checked library of formal theorems uses such numerical identities to confirm that its internal computations are consistent. The declaration does not prove any physical law, does not establish the Regge calculus approximation, and does not derive any constant of nature. It is a single, verified step in a much longer chain of formal work.

What the declaration does establish is precise: for the index tuple (2,0,0,0,1,3), the value of m2Num is exactly eight times the value of explicitZ. The equality is checked by the computer and holds without exception. This is a fact about the definitions inside the framework, not about the physical world.

theorem e_203333 : m2Num 2 0 3 3 3 3 = 8 * explicitZ 2 0 3 3 3 3 := by decide

theorem e_203333 : m2Num 2 0 3 3 3 3 = 8 * explicitZ 2 0 3 3 3 3 := by decide

What this page does not claim

This declaration does not prove any physical law or property of gravity. This declaration does not establish the Regge calculus approximation as physically correct. This declaration does not derive any constant of nature or fundamental parameter.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk08.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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