Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk05 E 110001

A numerical identity in the gravity analysis

The declaration e_110001 is a machine-checked proof of a specific numerical identity. It states that a quantity called m2Num, evaluated at a particular set of six indices, equals eight times another quantity called explicitZ at the same indices. The proof is carried out by the decide tactic, meaning the computer evaluates both sides and confirms they are equal. This is a formal, verified statement within the framework's library of theorems.

The identity is part of a larger analysis of gravity, specifically a chunk of a calculation involving the Regge exact midpoint and an identity called M2TTIdentity4D. The docstring for this chunk notes that it is the fifth chunk and that it contains 256 kernel decisions, which are individual cases that the computer checks. The declaration e_110001 is one of these cases, providing a verified numerical equality for a particular combination of indices.

In plain terms, this declaration does not establish a new physical law or a general mathematical theorem. It verifies a specific arithmetic fact that is a component of a broader computational proof. The statement is narrow: it confirms that for one particular set of input values, the two defined quantities agree. It does not claim that this identity holds for all inputs, nor does it derive any physical consequence from the equality.

Within the Recognition Science framework, this kind of declaration is a building block. It is a checked step in a larger chain of reasoning, ensuring that the numerical calculations are correct. The value of such a declaration is in its precision and its place within the formal system, not in any standalone physical insight it provides.

theorem e_113333 : m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3 := by decide

theorem e_113333 : m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3 := by decide

theorem e_113333 : m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3 := by decide

What this page does not claim

This declaration does not establish a general mathematical theorem that holds for all inputs. This declaration does not derive any physical consequence from the numerical equality. This declaration does not provide any standalone physical insight beyond its role as a verified computational step.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk05.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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