Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk13

The 256-case check

In numerical analysis, a Regge approach breaks spacetime into discrete simplices, the higher-dimensional analog of a grid of triangles. This verification step checks that a quantity called m2Num, computed at a specific midpoint, equals exactly 8 times another quantity called explicitZ, for a batch of 256 index combinations. The indices, such as 3 1 3 3 3 3, label the positions of the simplices in the grid.

This block, named chunk 13, is one part of a larger verification effort. The core statement is simple: for all 256 combinations of six indices where the first is 3 and the second is 1, the equation m2Num = 8 * explicitZ holds. Each of the 256 theorems, named e_313333 through e_313200, proves this equality for one specific index combination. The proof method is by decide, meaning the computer kernel directly computes both sides and confirms they are identical.

In plain language, this block establishes a precise numerical relationship that the broader theory expects. It is a piece of a much larger proof that the discrete gravity calculations behave consistently with the framework's predictions. The result is not an approximation; it is an exact equality, verified by a machine for every one of the 256 cases. This is the kind of check that builds confidence in a complex formal system, one chunk at a time.

theorem e_313333 : m2Num 3 1 3 3 3 3 = 8 * explicitZ 3 1 3 3 3 3 := by decide

What this page does not claim

This block does not prove the full gravity identity, only this specific chunk of 256 cases. This block does not derive the value of m2Num or explicitZ from first principles. This block does not make any claim about the physical correctness of the discrete gravity model.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk13.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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