Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk04 E 100001

A single arithmetic check

The declaration e_100001 is a single, machine-checked arithmetic fact. It states that a number called m2Num, evaluated at the index 1 0 0 0 0 1, equals 8 times another number called explicitZ at the same index. The proof is the word decide, which means the computer simply computed both sides and found them equal. This is not a physical law or a new force of nature; it is a bookkeeping check inside a much larger calculation.

The context is a gravity analysis. The names m2Num and explicitZ belong to a family of numbers used in a calculation about Regge calculus, a method that approximates curved spacetime by flat pieces, like a geodesic dome approximating a sphere. The declaration belongs to a chunk of 256 such checks, each verifying that one entry of m2Num is exactly 8 times the corresponding entry of explicitZ. The index 1 0 0 0 0 1 is just the position of this particular entry in that grid.

What the theorem proves is narrow but exact: for this one index, the equality holds. It does not prove the equality for all indices, and it does not explain why the factor 8 appears. The factor is part of the definition of m2Num, not a result derived from deeper principles. The declaration is a brick in a wall, not the wall itself.

In Recognition Science, this kind of check is routine. The framework's library of formal theorems stores thousands of such small, verified steps. Each one is a guarantee that a specific calculation was done correctly, with no hidden hand-waving. The value of e_100001 is that it removes one possible source of arithmetic error from the larger gravity analysis. It does not, by itself, say anything about the physical content of that analysis.

A reader who wants to know what the gravity calculation concludes must look elsewhere. This declaration only certifies that one number equals another number at one point. It is a receipt for a single transaction, not a theory of gravity.

theorem e_103332 : m2Num 1 0 3 3 3 2 = 8 * explicitZ 1 0 3 3 3 2 := by decide

theorem e_103332 : m2Num 1 0 3 3 3 2 = 8 * explicitZ 1 0 3 3 3 2 := by decide

theorem e_103332 : m2Num 1 0 3 3 3 2 = 8 * explicitZ 1 0 3 3 3 2 := by decide

What this page does not claim

This declaration does not prove the equality for any other index. This declaration does not explain why the factor 8 appears. This declaration does not establish any physical conclusion about gravity.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk04.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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