Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk02 E 020011

A single verified arithmetic step

A recognition event is a discrete record of an act of distinguishing one thing from another. The library in question is a machine-checked collection of formal theorems, and one of its declarations, e_020011, establishes a precise arithmetic identity for a particular six-index entry in a table called m2Num. The theorem states that m2Num 0 2 0 0 1 1 = 8 * explicitZ 0 2 0 0 1 1.

This is not a statement about physics. It is a statement about numbers. The declaration proves that a certain computed value, indexed by the six-tuple (0, 2, 0, 0, 1, 1), is exactly eight times the value of another computed quantity, explicitZ, at the same index. The proof is by direct computation, a method the machine checks without relying on any additional assumptions. The result is a theorem in the library's formal system, meaning it has been verified step by step.

The declaration is part of a larger file that contains many similar theorems, each for a different six-index tuple. Together, these theorems cover a block of entries in the m2Num table, establishing the factor of eight across that entire block. The declaration e_020011 is one such link in this chain, confirming the identity for its specific index.

What the declaration does not claim is any physical interpretation. It does not say what m2Num or explicitZ represent, nor does it claim that the factor of eight has any meaning in the theory of gravity. It only asserts the arithmetic fact. The broader framework may use this table in further derivations, but this single declaration is confined to the numbers themselves.

theorem e_023233 : m2Num 0 2 3 2 3 3 = 8 * explicitZ 0 2 3 2 3 3 := by decide

theorem e_023233 : m2Num 0 2 3 2 3 3 = 8 * explicitZ 0 2 3 2 3 3 := by decide

What this page does not claim

This declaration does not assign physical meaning to m2Num or explicitZ. This declaration does not prove any property about gravity or spacetime. This declaration does not establish the factor of eight for any index other than the one stated.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk02.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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