Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk15 E 330013

A computed identity

The declaration e_330013 is a machine-checked proof of a single arithmetic identity. It states that a function called m2Num, evaluated at a particular six-digit input, equals eight times another function called explicitZ at the same input. The proof is carried out by the computer's own decision procedure, meaning the equality is verified by direct computation, not by a hand-written argument. This is one of many such identities in a file that checks a large batch of similar cases.

The context is a calculation in the Recognition Science framework's gravity analysis. The framework models physical structure as arising from a discrete record of recognition events, and this file appears to be part of a numerical check on a proposed identity involving a quantity called m2Num. The specific input, 3 3 3 3 3 3 in the example shown, is one of 256 possible six-digit combinations. The docstring describes this as chunk 15 of a larger verification, where the kernel decides each case.

What the declaration does not claim is just as important. It does not state that m2Num has any physical meaning, nor that the identity holds for all inputs. It only verifies the equality for the specific inputs listed in the file. The proof does not explain why the identity holds, only that it does for these cases. It is a computational check, not a derivation of a law or a statement about the physical world.

In the Recognition Science framework, this kind of verification is a routine but essential step. The framework's library contains many such machine-checked theorems, and each one adds confidence that the larger mathematical structure is consistent. This particular declaration is a small piece of that structure, confirming a pattern in the numbers without asserting what the pattern means.

theorem e_333333 : m2Num 3 3 3 3 3 3 = 8 * explicitZ 3 3 3 3 3 3 := by decide

theorem e_333333 : m2Num 3 3 3 3 3 3 = 8 * explicitZ 3 3 3 3 3 3 := by decide

theorem e_333333 : m2Num 3 3 3 3 3 3 = 8 * explicitZ 3 3 3 3 3 3 := by decide

What this page does not claim

This declaration does not assign any physical meaning to the functions m2Num or explicitZ. This declaration does not prove that the identity holds for any input other than the specific ones listed in the file. This declaration does not explain why the identity holds, only that it does for these cases.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk15.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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