Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk09 E 210002

A single numerical check

In the Recognition Science framework's machine-checked library of formal theorems, a declaration named e_210002 is one of hundreds of small, concrete checks. It states that a particular numerical expression, written m2Num 2 1 0 0 0 2, equals eight times another expression, explicitZ 2 1 0 0 0 2. The proof is by direct computation, using the decide tactic, which means the kernel verified the equality by evaluating both sides step by step.

This is not a general law of physics or a new derivation. It is a single instance of a larger identity that the framework is checking across many index combinations. The expression m2Num and explicitZ are part of a family of functions used in the framework's gravity analysis, specifically in a four-dimensional Regge calculus context. The theorem confirms that for this one set of indices, the two functions agree up to the factor of eight. The docstring for the chunk says m2Num = 8·explicitZ, and this theorem is one of the many cases that makes that statement concrete.

The value of this declaration is not in the arithmetic itself, which is trivial, but in what it represents: a verified, auditable step in a much larger chain of formal reasoning. Each such theorem, checked by the kernel, builds confidence that the framework's computations are correct. It does not, by itself, prove anything about gravity, about the four-dimensional nature of space, or about the physical content of the m2Num and explicitZ functions. It is a piece of the machine-checked scaffolding, not a standalone result about the world.

theorem e_213333 : m2Num 2 1 3 3 3 3 = 8 * explicitZ 2 1 3 3 3 3 := by decide

theorem e_213333 : m2Num 2 1 3 3 3 3 = 8 * explicitZ 2 1 3 3 3 3 := by decide

What this page does not claim

This declaration does not prove any general property of gravity or of four-dimensional space. It does not establish the physical meaning of the m2Num or explicitZ functions. It does not claim that the factor of eight holds for all index combinations, only for this specific one.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk09.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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