Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk03

A numerical ledger check

Numerical analysis often ends with a table of numbers. The question is whether those numbers are consistent with the formula they claim to represent. This file is a machine-checked verification of one such table in a gravity calculation, and it establishes that a specific numerical array, called m2Num, is exactly eight times another array, called explicitZ, for a block of 38 entries. Each entry is a rational number, and the proof is a direct computation, not an approximation.

The setting is a discrete model of gravity, where spacetime is built from simple geometric pieces rather than smooth curves. In this model, the calculation involves a midpoint rule and a quantity called m2, which appears in an identity related to the trace of the metric. The file name encodes this: Regge refers to the discrete gravity framework, exact midpoint to the numerical method, and M2TTIdentity4D to the specific identity being checked in four dimensions. The final part, Dm2NumChunk03, simply labels this as the third chunk of a larger numerical verification.

What the file proves is a set of theorems of the form m2Num 0 3 3 3 3 3 = 8 * explicitZ 0 3 3 3 3 3, and similarly for the other 37 combinations of indices. The indices are the coordinates of the numerical grid. The factor of eight is not an accident; it is part of the definition of m2Num, as stated in the file's docstring: m2Num = 8·explicitZ. The proof method is 'by decide', which means the computer checks the equality by evaluating both sides and confirming they are the same exact rational number.

In plain language, this file is a receipt. It confirms that a particular column of numbers in a larger gravity calculation was computed correctly, according to its own definition. It does not prove anything about gravity itself, nor does it derive the identity from first principles. It is a local consistency check, a small but necessary step in a larger formal verification effort. The value is in the certainty: a human could make an arithmetic error, but a machine-checked proof of this form is exact.

Within Recognition Science, this kind of check is part of building a ledger, a discrete record of events and their costs, for gravity. The framework's broader claims about gravity rest on many such verified numerical facts. This file contributes one small, solid stone to that foundation, and it shows the standard of rigor the framework aims for: every number in the table is backed by a proof, not by a promise.

theorem e_033333 : m2Num 0 3 3 3 3 3 = 8 * explicitZ 0 3 3 3 3 3 := by decide

theorem e_033333 : m2Num 0 3 3 3 3 3 = 8 * explicitZ 0 3 3 3 3 3 := by decide

What this page does not claim

This file does not prove any physical law about gravity. This file does not derive the M2TTIdentity4D identity from first principles. This file does not establish that the numerical table covers all possible grid points.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk03.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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