Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk14 E 320012

A numerical identity in a gravity proof

The declaration e_320012 is a verified arithmetic identity inside a large formal proof about gravity. It states that a certain numerical function, called m2Num, evaluated at the six arguments 3 2 3 2 0 0, equals eight times another function, explicitZ, evaluated at the same six arguments. The proof is a direct computation, marked by the keyword decide, which means the machine checked the equality by calculation rather than by a chain of abstract reasoning.

This identity belongs to a family of similar statements, all in the same file, each covering a different combination of six small numbers. The file's title mentions Regge calculus, a lattice approach to general relativity where spacetime is approximated by flat building blocks. The name "midpoint" suggests the evaluation points are chosen at the centers of these blocks. The broader context is a project that uses a machine-checked library of formal theorems to verify the steps of a gravitational calculation.

What does this specific declaration establish? Only that the equality holds for the one set of arguments. It does not prove the identity for all arguments, nor does it derive any physical law. It is a single brick in a wall: the wall might be a theorem about gravity, but this declaration alone confirms just one numerical relationship. The value 8 appears because the calculation likely involves a factor of two per spatial dimension, but the declaration itself does not explain why the factor is there.

The declaration does not claim that the identity is physically meaningful, that it matches any experiment, or that it applies beyond the exact six arguments given. It is a formal statement about two defined functions, checked by computation. A reader should not infer from this declaration alone that gravity has been derived or that any physical constant has been explained. The declaration is a verification of arithmetic, not a statement about the world.

theorem e_323200 : m2Num 3 2 3 2 0 0 = 8 * explicitZ 3 2 3 2 0 0 := by decide

theorem e_323200 : m2Num 3 2 3 2 0 0 = 8 * explicitZ 3 2 3 2 0 0 := by decide

What this page does not claim

The declaration does not prove the identity for all possible arguments. The declaration does not establish any physical law or match any experiment. The declaration 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/ReggeExactMidpointM2TTIdentity4DM2NumChunk14.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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: