Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk13 E 310010

A single checked identity

The declaration e_310010 is one entry in a long list of machine-checked arithmetic identities. Each identity states that a particular numerical expression, written m2Num with six indices, equals eight times another expression, written explicitZ with the same six indices. The proof is the word "decide," which means a computer program checked the arithmetic directly and found the two sides equal. This is a formal verification step, not a derivation from physical principles.

The wider context is a project to verify a large set of such identities, organized into chunks. The declaration belongs to a chunk labeled 13, and the surrounding text notes that this chunk contains 256 such checks. Each check is independent: it confirms one specific numerical equality and says nothing about the meaning of the numbers or their physical interpretation. The names m2Num and explicitZ are internal labels within the verification library; the declaration itself does not explain what they represent.

What the declaration does not claim is just as precise as what it claims. It does not assert that the equality holds for all possible indices, only for the six specific values 3, 1, 0, 0, 1, 0. It does not state that m2Num and explicitZ are equal as functions, only that their values agree at this one point. It does not connect the identity to any physical quantity, such as a mass or a coupling constant. The declaration is a single verified arithmetic fact, and its role is to build confidence in a larger body of formal work, one checked step at a time.

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

The declaration does not claim that m2Num and explicitZ are equal as functions. The declaration does not claim any physical interpretation for the numbers involved. The declaration does not claim that the identity holds for any other choice of indices.

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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: