Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk14 E 320010

A kernel-checked arithmetic check

The declaration e_320010 is a formal theorem in the Recognition Science framework's machine-checked library of formal theorems. It states that for the six-index argument (3,2,0,0,1,0), the function m2Num equals 8 times the function explicitZ applied to the same six arguments. In plainer terms, it verifies a specific arithmetic identity: m2Num 3 2 0 0 1 0 = 8 * explicitZ 3 2 0 0 1 0.

The proof is by the `decide` tactic, meaning the Lean kernel computes both sides and confirms they are equal. This is not a derivation from physical principles; it is a direct computational check of one instance in a larger family of identities. The docstring notes this is part of "m2Num = 8·explicitZ, chunk 14 (256 kernel decides)", indicating the declaration is one of many similar checks in a batch.

In Recognition Science, this kind of theorem plays a role in verifying that a numerical function used in gravity analysis matches a scaled reference function across many inputs. The framework models physical structure through such exact arithmetic identities, and machine-checked proofs ensure the calculations are correct. However, the declaration itself says nothing about what m2Num or explicitZ represent physically; it only establishes the numerical equality for this specific input.

What the declaration does not claim is broader than what it does. It does not assert that the identity holds for all six-index arguments; that would require a separate universal theorem. It does not define the physical meaning of the functions involved. It does not connect to any measurement or empirical prediction. It is precisely one verified arithmetic fact, useful as a building block but carrying no physical interpretation by itself.

theorem e_323333 : m2Num 3 2 3 3 3 3 = 8 * explicitZ 3 2 3 3 3 3 := by decide

What this page does not claim

The declaration does not prove the identity for all inputs, only for the specific argument (3,2,0,0,1,0). The declaration does not assign physical meaning to the functions m2Num or explicitZ. The declaration does not make any empirical prediction or connect to measured values.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk14.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: