Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk02 E 020013

A machine-checked arithmetic fact

A formal theorem is a statement that a computer program has checked from the rules of logic, with no gaps. The declaration e_020013 is one such theorem. It states a specific arithmetic identity: for a particular set of six indices, the value of a function called m2Num equals 8 times the value of a function called explicitZ. The theorem is proved by the word decide, which means the computer simply calculated both sides and found them equal.

This identity is part of a larger collection. The file containing it, ReggeExactMidpointM2TTIdentity4DM2NumChunk02, holds a chunk of 256 such identities, each for a different set of six indices. The indices run from 0 to 3, and the first index is always 0. The collection as a whole is part of the framework's work on gravity, specifically on a calculation called the Regge exact midpoint M2 TT identity in four dimensions. The name suggests the identity is a piece of a proof that a certain quantity, m2Num, is exactly 8 times another quantity, explicitZ, across a grid of index values.

In plain terms, this declaration does not prove anything about gravity itself. It proves a fact about arithmetic. It is a single, small, machine-checked step in a larger formal development. The larger development may aim to establish a physical result, but this particular theorem only certifies that one number equals another number, for one combination of indices. It is a building block, not the building.

The value of such a declaration is that it is a verified, exact statement. There is no approximation, no hand-waving, no appeal to intuition. The computer checked it. This is the kind of fact that a large proof chain can rely on without re-checking it by hand. It is the granular, unglamorous work that makes a large formal proof trustworthy.

theorem e_023333 : m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3 := by decide

theorem e_023333 : m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3 := by decide

theorem e_023333 : m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3 := by decide

What this page does not claim

This declaration does not prove any physical fact about gravity. This declaration does not establish the identity for indices other than the one specified. This declaration does not explain what m2Num or explicitZ represent physically.

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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