Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk06 E 120013

A kernel-checked arithmetic identity

The declaration e_120013 is a theorem in the Recognition Science framework's machine-checked library of formal theorems. It states that for the index tuple (1,2,0,0,1,3), the value of the function m2Num equals 8 times the value of the function explicitZ for the same tuple. The proof is the single word "decide", meaning the computer kernel directly computed both sides and found them equal; no further argument was needed.

This identity belongs to a large family of similar statements, each covering one six-index combination. The file containing e_120013 lists dozens of such theorems, all sharing the same form: m2Num i j k l m n = 8 * explicitZ i j k l m n. Each is proved in the same way, by direct computation. The collection is part of a broader effort to verify, step by step, an identity involving the function m2Num across all its index values.

In Recognition Science, the framework models physical structure through a discrete record of recognition events, called a ledger, and derives constants and laws from the cost of recognition. This particular theorem does not derive any new physics. It is a computational check, a single tile in a mosaic. Its role is to confirm that for the specific index (1,2,0,0,1,3), the numerical relationship holds exactly, as the kernel's computation attests.

What the theorem does not claim is broader significance on its own. It does not assert that the identity holds for all index tuples; that would require a separate, general theorem. It does not interpret what m2Num or explicitZ physically mean; the declaration only states their numerical equality. It does not prove any property of gravity, recognition, or the framework's constants. It is a precise, narrow, and fully verified arithmetic fact, valuable only as part of a larger verified whole.

theorem e_123213 : m2Num 1 2 3 2 1 3 = 8 * explicitZ 1 2 3 2 1 3 := by decide

theorem e_123213 : m2Num 1 2 3 2 1 3 = 8 * explicitZ 1 2 3 2 1 3 := by decide

What this page does not claim

This theorem does not establish the identity for all index tuples; it covers only the tuple (1,2,0,0,1,3). This theorem does not assign physical meaning to m2Num or explicitZ. This theorem does not prove any property of gravity, recognition, or the framework's derived constants.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk06.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: