Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk13 E 310002

A numerical identity in a gravity proof

The declaration e_310002 is a small, exact arithmetic fact inside a large machine-checked library of formal theorems. It states that a function called m2Num, evaluated at a particular set of six arguments, equals 8 times another function called explicitZ evaluated at the same arguments. In plain language, it verifies that a certain computed quantity is exactly eight times a reference quantity, for one specific combination of inputs.

The proof of this fact is entirely computational. The declaration is proved by the word decide, which means the machine checked the equality by direct calculation, without any symbolic reasoning or assumptions. This is the most basic kind of proof: it confirms that two arithmetic expressions are equal by evaluating them. The specific arguments, such as 3 1 3 3 3 3, are indices that select a particular entry in a larger table of values.

This declaration is part of a larger project called ReggeExactMidpointM2TTIdentity4D, which appears to be a verification of a mathematical identity related to the Regge calculus formulation of general relativity in four dimensions. The name suggests the identity holds at a midpoint of a Regge spacetime, and that it involves a quantity called M2. The declaration e_310002 is one of many similar declarations in a chunk of the proof, each checking the same type of relation for different index values.

In Recognition Science, the framework's library uses such machine-checked declarations to build confidence in large calculations. The declaration e_310002 does not, by itself, prove any physical law or establish any new mathematical theorem. It only confirms a single arithmetic relation. The broader significance, if any, comes from the context: it is a small piece of a much larger proof that aims to verify a complete identity. The declaration itself carries no physical interpretation; it is a purely formal statement about numbers.

What this declaration does not claim is also clear. It does not claim that the identity holds for all possible inputs, only for the specific set of arguments listed. It does not claim that the functions m2Num and explicitZ have any physical meaning, nor that the overall project has been completed. It is a single verified step, not a conclusion. The value of such declarations lies in their precision and their role in a larger, machine-checked argument.

theorem e_313333 : m2Num 3 1 3 3 3 3 = 8 * explicitZ 3 1 3 3 3 3 := by decide

theorem e_313333 : m2Num 3 1 3 3 3 3 = 8 * explicitZ 3 1 3 3 3 3 := by decide

What this page does not claim

This declaration does not prove the identity for all possible inputs, only for the specific set of arguments listed. This declaration does not assign any physical meaning to the functions m2Num or explicitZ. This declaration does not establish the validity of the entire ReggeExactMidpointM2TTIdentity4D project.

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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