Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk00 E 000001

A single verified entry

The declaration e_000001 is one entry in a large machine-checked library of formal theorems. It states a specific equality: for the index pattern 0 0 0 0 0 1, the quantity m2Num 0 0 0 0 0 1 equals 8 times explicitZ 0 0 0 0 0 1. The proof is marked by the word decide, meaning the kernel verified the equality by direct computation, with no additional axioms or assumptions. This is a local, concrete fact about two defined numerical functions, not a general law.

The context names the file as part of a gravity analysis, specifically a Regge exact midpoint calculation for a four-dimensional identity. The pattern of indices, six entries each taking values 0 through 3, suggests these are components of a tensor-like object with six slots. The equality being checked is that one component, m2Num, is exactly eight times another, explicitZ, for this particular index combination. The theorem does not say what m2Num or explicitZ represent physically; it only certifies the arithmetic relationship between them at this one point.

This theorem is one of many similar declarations in the same file, each covering a different index pattern such as 0 0 3 3 3 3 or 0 0 3 2 1 0. Together they form a chunk of 256 such checks, as the file's docstring notes. The role of e_000001 is to contribute one verified tile to that larger mosaic. It establishes that for this specific index, the two functions stand in the ratio 8 to 1, nothing more and nothing less.

What the declaration does not claim is just as precise. It does not assert that the ratio 8 holds for all indices, nor does it explain why the factor 8 appears. It offers no interpretation of the functions in terms of physical gravity, curvature, or any observable phenomenon. The theorem is silent on whether m2Num or explicitZ correspond to measurable quantities. Its entire content is the verified equality for the single index pattern 0 0 0 0 0 1, checked by the kernel's computation.

theorem e_003333 : m2Num 0 0 3 3 3 3 = 8 * explicitZ 0 0 3 3 3 3 := by decide

theorem e_003333 : m2Num 0 0 3 3 3 3 = 8 * explicitZ 0 0 3 3 3 3 := by decide

What this page does not claim

The theorem does not claim the ratio 8 holds for any index other than 0 0 0 0 0 1. It does not claim any physical interpretation for m2Num or explicitZ. It does not assert the identity has been derived from first principles rather than verified by computation.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk00.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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