Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk09 E 210001

A verified arithmetic identity

The declaration e_210001 is a theorem in a machine-checked library of formal theorems. Its statement is a precise arithmetic identity: for a certain function m2Num evaluated at six indices, the result equals 8 times another function explicitZ evaluated at the same six indices. The proof is by decide, which means the computer simply computes both sides and verifies they are equal. This is a concrete, checkable fact about numbers, not a claim about the physical world.

The identity is part of a larger file called ReggeExactMidpointM2TTIdentity4DM2NumChunk09. The name suggests it belongs to a series of similar identities, and indeed the file contains dozens of theorems with the same shape, each for a different choice of six indices. The docstring says this is chunk 9 of a computation involving 256 kernel decisions. Each theorem in the file is a small, self-contained step: it verifies one instance of the pattern m2Num = 8 * explicitZ.

What the declaration does not claim is just as important. It does not assert that the functions m2Num or explicitZ represent anything about gravity, spacetime, or any physical quantity. The names of the file and the functions come from a broader research program, but this theorem itself is purely about the equality of two computed numbers. It does not prove that the pattern holds for all indices, only for the specific six-tuple in its statement. It does not derive any physical law, and it does not connect to any measured value.

In plain terms, e_210001 is a verified arithmetic fact. Its value lies in being a checked step in a larger formal development, not in any standalone physical meaning. A reader should treat it as a building block: reliable, exact, but narrow in scope.

theorem e_213333 : m2Num 2 1 3 3 3 3 = 8 * explicitZ 2 1 3 3 3 3 := by decide

theorem e_213333 : m2Num 2 1 3 3 3 3 = 8 * explicitZ 2 1 3 3 3 3 := by decide

theorem e_213333 : m2Num 2 1 3 3 3 3 = 8 * explicitZ 2 1 3 3 3 3 := by decide

What this page does not claim

The declaration does not claim that m2Num or explicitZ have any physical meaning. The declaration does not prove the identity holds for indices other than the one stated. The declaration does not derive any law of gravity or any measured physical value.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk09.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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