Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk00 E 000012

A single checked identity

The declaration e_000012 is one entry in a large table of arithmetic identities. Each identity states that a number called m2Num, evaluated at six indices, equals eight times a number called explicitZ at the same six indices. The specific identity e_000012 covers the index tuple (0, 0, 3, 2, 2, 1), so it reads: m2Num 0 0 3 2 2 1 = 8 * explicitZ 0 0 3 2 2 1.

These indices are not random. They label components of a four-dimensional object, likely a tensor or a grid of values, that arises in an exact midpoint analysis of gravity. The factor of eight is a fixed scaling between the two arrays. The proof method is direct computation: the command decide tells the machine-checked library of formal theorems to evaluate both sides and confirm they match, with no intermediate lemmas.

In Recognition Science, this identity is part of a larger verification effort. The framework models physical structure through a discrete ledger, a record of recognition events, and here it checks that a numerical component of its gravity analysis satisfies the expected proportionality. The theorem is axiom-clean: it relies only on the ambient type theory's standard postulates, with no framework-specific axioms added.

The practical consequence is narrow but solid. For this one component, the computed value matches the scaled reference exactly. The identity does not assert anything about other index tuples, does not interpret the numbers physically, and does not establish that the overall gravity analysis is correct. It is a single, verified row in a much larger table.

theorem e_003221 : m2Num 0 0 3 2 2 1 = 8 * explicitZ 0 0 3 2 2 1 := by decide

theorem e_003221 : m2Num 0 0 3 2 2 1 = 8 * explicitZ 0 0 3 2 2 1 := by decide

What this page does not claim

This identity does not establish any property about other index tuples or the full m2Num array. This identity does not provide a physical interpretation of the numbers involved. This identity does not validate the overall gravity analysis or its assumptions.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk00.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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