Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk12 E 300013

A verified arithmetic step

The declaration e_300013 is a theorem in the Recognition Science framework's machine-checked library of formal theorems. It states a specific arithmetic fact: for a particular set of six input numbers, the function m2Num returns exactly eight times the value of the function explicitZ. The proof is carried out by the computer's kernel, which directly evaluates both sides and confirms they are equal. This is a fully verified computation, not an approximation or a hand-checked claim.

This theorem is part of a much larger effort: the framework is building a complete, machine-checked derivation of physics from first principles. Within that effort, the declaration e_300013 is a single, small brick in a wall. It belongs to a chunk of the library that verifies a large number of similar identities, each one checking that a numerical function called m2Num behaves as expected for a grid of input values. The specific pattern here, that m2Num equals eight times explicitZ, is one of many such checks that together support a broader identity about how these functions relate.

The declaration does not claim anything about the physical meaning of the numbers involved. It does not say that m2Num represents a force, a mass, or any specific physical quantity. It does not claim that the identity holds for all possible inputs; it only verifies the equality for the specific six-number combination named in the theorem. The theorem is a statement about the internal consistency of the framework's definitions, not a statement about the external world. It is a check that the machinery works as intended at the most basic level.

In Recognition Science, this kind of granular verification is the point. The framework's library proves theorems by breaking them down into steps so small that a computer can check each one. A declaration like e_300013 is the smallest possible unit of that process: a single, confirmed arithmetic fact. It is the kind of result that gives the larger, more ambitious claims of the framework their foundation, one verified step at a time.

theorem e_303333 : m2Num 3 0 3 3 3 3 = 8 * explicitZ 3 0 3 3 3 3 := by decide

theorem e_303333 : m2Num 3 0 3 3 3 3 = 8 * explicitZ 3 0 3 3 3 3 := by decide

What this page does not claim

The declaration does not claim that the identity holds for all possible inputs, only for the specific six-number combination named in the theorem. The declaration does not assign any physical meaning to the functions m2Num or explicitZ. The declaration does not claim to derive any physical law or constant; it only confirms a single arithmetic equality.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk12.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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