Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk12 E 300003

A block of verified arithmetic

The declaration e_300003 is one small piece of a much larger, machine-checked calculation in the Recognition Science framework. Its statement is a precise arithmetic identity: for a particular set of six indices, the value of the function m2Num equals eight times the value of the function explicitZ. The proof is a direct computation, noted in the source as 'by decide', meaning the Lean 4 proof assistant verified it by evaluating both sides. This is not a new physical law; it is a verified numerical fact, a single checked cell in a grid of similar identities.

This identity belongs to a batch of theorems, each with a name like e_303333 or e_303332, that together form 'chunk 12' of a larger project. The project's name, ReggeExactMidpointM2TTIdentity4D, suggests it concerns an exact identity at the midpoint of a Regge calculus calculation in four dimensions. Regge calculus is a lattice approach to general relativity, where spacetime is approximated by flat simplices. The function m2Num likely computes a numerical quantity, while explicitZ is probably a reference or closed-form expression. The identity states that for these indices, the computed value is exactly eight times the reference value.

The role of such a theorem is to provide a rigorous, machine-verified foundation for a longer chain of reasoning. In a large formal proof, it is not enough to assert that a calculation is correct; every step must be justified. This theorem, and its siblings in the same chunk, serve as that justification for a specific set of numerical cases. They are the load-bearing arithmetic that allows the larger argument to proceed without a gap.

In Recognition Science, the framework's library of formal theorems is a collection of such machine-checked results. This declaration is a single entry in that library. It establishes a fact about the functions m2Num and explicitZ, nothing more. It does not, by itself, prove any physical statement about gravity, nor does it define what those functions mean. Its meaning is entirely contained in the arithmetic relation it states.

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

This declaration does not establish any new physical law or property of gravity. This declaration does not define the functions m2Num or explicitZ. This declaration does not verify the identity for all possible indices, only for the specific set named in the theorem.

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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