Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk06 E 120012

A machine-checked arithmetic identity

The declaration e_120012 is a small, machine-checked theorem inside a larger formal verification project. It states that for a specific set of six indices, the value of a function called m2Num equals eight times the value of another function called explicitZ at the same indices. In plain terms, it confirms a precise arithmetic relationship between two quantities that appear in a calculation related to gravity.

The theorem is one of many similar statements in a file that checks a whole block of these identities. Each one handles a different combination of six indices, and each is proved by the same method: direct computation, or "by decide" in the formal language. This means the proof does not rely on a chain of abstract reasoning; it simply evaluates both sides of the equation and confirms they match. The declaration e_120012 specifically covers the indices 1, 2, 0, 0, 1, 2, establishing that m2Num 1 2 0 0 1 2 = 8 * explicitZ 1 2 0 0 1 2.

What this does not claim is broader significance. The theorem does not say what m2Num or explicitZ physically mean, nor does it explain why the factor of eight appears. It does not assert that the whole gravity calculation is correct; it only verifies one arithmetic step within it. The declaration is a building block, not a standalone result about physics.

In the context of the Recognition Science framework, this is part of a machine-checked library of formal theorems. The value of such a declaration is that it removes any doubt about this particular computation. A reader can trust that the arithmetic is correct, without needing to redo the calculation by hand. The broader question of what the calculation represents, and whether it matches physical reality, is left to other parts of the framework.

theorem e_123201 : m2Num 1 2 3 2 0 1 = 8 * explicitZ 1 2 3 2 0 1 := by decide

What this page does not claim

This theorem does not establish any physical meaning for m2Num or explicitZ. This theorem does not verify the correctness of the entire gravity calculation. This theorem does not explain why the factor of eight appears.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk06.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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