Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk12 E 300012

A single arithmetic check

In a large formal calculation, thousands of small arithmetic facts must be verified one by one. The declaration e_300012 is one such verification. It checks a single entry in a table of numbers called m2Num, which appears in a gravity analysis module. The entry is indexed by six digits, 3 0 0 0 1 2, and the theorem states that the value of m2Num at that index equals 8 times the value of another table, explicitZ, at the same index. The proof is a direct computation, marked by the keyword decide, which means the computer evaluates both sides and confirms they match.

This is a routine but necessary step. The larger project, Recognition Science, builds a machine-checked library of formal theorems. Within that library, a gravity analysis file works through an identity involving a quantity called m2Num. The file is divided into chunks, and this chunk, number 12, contains a block of such equalities. Each equality has the same shape: m2Num at some six-digit index equals 8 times explicitZ at that same index. The declaration e_300012 is one of these, and its proof is by direct computation, not by a deep theorem.

In Recognition Science, the framework models physical structure as a discrete record of recognition events, and this gravity calculation is part of testing that model against a known identity. The identity itself, that m2Num equals 8 times explicitZ, is a structural relation within the calculation. The declaration e_300012 verifies that relation for one specific index. It does not establish the identity for all indices, nor does it interpret what the numbers mean physically. It is a single, concrete, verified fact.

What e_300012 does not claim is broader than what it claims. It does not prove the entire gravity identity, which would require checking every index. It does not connect the numbers to any physical measurement or observation. It does not say anything about the meaning of the tables m2Num or explicitZ beyond their numerical values. The declaration is a building block, not a conclusion. Its value lies in being one more verified stone in a wall of formal proof.

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 prove the entire gravity identity for all indices. This declaration does not connect the numerical tables to any physical measurement. This declaration does not interpret the physical meaning of the numbers.

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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