Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk13 E 310001

A single arithmetic check

The declaration e_310001 is one small, precisely scoped result inside a much larger machine-checked library of formal theorems. Its entire content is an arithmetic identity: for a particular set of six index values, the number computed by a function called m2Num equals eight times the number computed by a function called explicitZ. The theorem states this equality and proves it by the most direct possible method: the computer evaluates both sides and confirms they are identical.

To see what this means, consider the identity in its full form. For the indices 3, 1, 0, 0, 0, 1, the theorem asserts that m2Num 3 1 0 0 0 1 = 8 * explicitZ 3 1 0 0 0 1. The proof is a direct computation, not a chain of abstract reasoning. It verifies that for this one combination of inputs, the two functions stand in an eightfold relationship. The declaration is part of a larger collection, chunk 13, which checks the same pattern across many index combinations, all with the same computational method.

In the context of the Recognition Science framework, this declaration is a piece of internal bookkeeping. The framework models physical structure through a ledger, a discrete record of recognition events, and this theorem checks that a specific numerical relationship holds within that model. The identity itself is not a physical law; it is a consistency check on the framework's own definitions. The theorem does not say what m2Num or explicitZ represent physically, nor does it connect this particular equality to any measurement or observation.

What the declaration does not claim is equally important. It does not state that this identity holds for all possible inputs, only for the one listed combination. It does not derive the value of any physical constant, nor does it predict an experimental outcome. It does not say that the eightfold relationship has any meaning beyond the definitions of the two functions. The theorem is a verified arithmetic fact, nothing more and nothing less.

theorem e_313301 : m2Num 3 1 3 3 0 1 = 8 * explicitZ 3 1 3 3 0 1 := by decide

theorem e_313301 : m2Num 3 1 3 3 0 1 = 8 * explicitZ 3 1 3 3 0 1 := by decide

What this page does not claim

This declaration does not prove that the identity holds for all possible index values. This declaration does not assign any physical meaning to the numbers it computes. This declaration does not derive or predict any measured physical constant.

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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