Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk10

A numerical identity, checked by brute force

In numerical analysis, an identity is a statement that two different ways of computing the same quantity always give the same answer. The module named gravity analysis Regge exact midpoint m2 ttidentity4 dm2 num chunk10 is one small piece of such a verification. It checks that a quantity called m2Num, which comes from a discrete approximation to a gravity equation, equals 8 times another quantity called explicitZ, for a specific block of index values.

The indices here run over a six-component list, and the chunk covers the 40 combinations where the first two indices are 2 and 2, and the third is 3. For each combination, the module states a theorem of the form m2Num 2 2 3 a b c = 8 * explicitZ 2 2 3 a b c, where a, b, and c each range from 0 to 3. The proof in each case is the single word "decide", which means the computer evaluates both sides directly and confirms they are equal. This is not a symbolic derivation; it is a brute-force numerical check, but one that is fully machine-verified.

The purpose of such a chunk is to build confidence in a larger claim. If the identity holds for every index combination in this block, and if other chunks cover the remaining combinations, then the full identity m2Num = 8 * explicitZ is established for all allowed inputs. The number 8 is not arbitrary; it appears as a constant factor in the relationship. The module does not explain why the factor is 8 or what the quantities physically mean; it only certifies that the arithmetic matches.

In Recognition Science, this kind of verification is part of a broader program. The framework derives physical structure from a forced cost function, and it uses a machine-checked library of formal theorems to keep every step auditable. This particular module is a low-level brick: it does not prove a law of physics, but it confirms that a computational identity holds exactly, with no rounding error and no hidden assumption. A reader can trust that the identity is true for these 40 cases because the computer checked each one.

The practical consequence is that any larger theorem relying on this identity for these index values now has a solid foundation. If a later proof uses m2Num 2 2 3 1 2 0, it can cite this chunk and know the value equals 8 * explicitZ 2 2 3 1 2 0. The module removes a potential source of error from the chain of reasoning, one index combination at a time.

theorem e_223333 : m2Num 2 2 3 3 3 3 = 8 * explicitZ 2 2 3 3 3 3 := by decide

theorem e_223333 : m2Num 2 2 3 3 3 3 = 8 * explicitZ 2 2 3 3 3 3 := by decide

What this page does not claim

This module does not derive the factor 8 or explain the physical meaning of the quantities. This module does not prove the identity for index combinations outside the 40 cases listed. This module does not establish any law of gravity; it only certifies a numerical identity.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk10.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.

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