Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk03 E 030013

A numerical identity

This page concerns a specific declaration, e_030013, inside a machine-checked library of formal theorems. The declaration is a small numerical identity. It states that a function called m2Num, evaluated at the six arguments 0, 3, 0, 0, 1, 3, equals eight times the value of another function, explicitZ, at the same six arguments. In symbols, the theorem reads m2Num 0 3 0 0 1 3 = 8 * explicitZ 0 3 0 0 1 3. The proof is by decide, meaning the computer checked the equality by direct computation.

The two functions belong to a larger project in the framework's library: the study of a four-dimensional identity, named ReggeExactMidpointM2TTIdentity4D. The names suggest the identity concerns a discrete version of gravity, built on a lattice of points, where a quantity called m2Num is compared against a reference value explicitZ. The factor of eight appears throughout this chunk of the library; many nearby declarations, such as e_033333 and e_033332, assert the same pattern for different arguments. The declaration e_030013 is one of hundreds of such entries, each a single line of the table.

In plain language, e_030013 establishes exactly one fact: for this particular choice of six indices, the computed value m2Num is eight times the reference value explicitZ. It does not prove the identity for all indices, and it does not explain why the factor of eight appears. It is a building block, not a general law. The declaration's scope is limited to the specific arguments it names.

Within the Recognition Science framework, this declaration is part of a larger effort to verify a four-dimensional identity by checking many individual cases. The framework's library contains the declaration as a theorem, meaning the equality is machine-checked and axiom-clean. But the theorem's content is narrow: it says nothing about the physical meaning of the functions, the origin of the factor of eight, or whether the pattern extends beyond the checked cases.

theorem e_033333 : m2Num 0 3 3 3 3 3 = 8 * explicitZ 0 3 3 3 3 3 := by decide

theorem e_033333 : m2Num 0 3 3 3 3 3 = 8 * explicitZ 0 3 3 3 3 3 := by decide

What this page does not claim

The declaration does not prove the identity for all possible six-index arguments. The declaration does not explain the origin or meaning of the factor of eight. The declaration does not establish any physical law about gravity; it only verifies a numerical equality.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk03.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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