Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk07 E 130001

A single verified identity

The declaration e_130001 is a formal theorem in the Recognition Science framework's machine-checked library of formal theorems. It states a precise numerical identity: the value of a function called m2Num at the six arguments 1, 3, 0, 0, 0, 1 equals eight times the value of another function called explicitZ at the same six arguments. In symbols, the theorem reads m2Num 1 3 0 0 0 1 = 8 * explicitZ 1 3 0 0 0 1. The proof is by direct computation: the computer checks that the two sides are equal. This is a single, exact fact, not an approximation.

The identity lives in a file dedicated to a Regge calculation, a lattice approach to general relativity where spacetime is built from flat triangular pieces. The file name mentions an exact midpoint and a four-dimensional identity. The m2Num function likely computes a numerical quantity from six indices, and explicitZ likely computes a related reference value. The theorem asserts that, for this particular choice of indices, the two are related by the factor eight. The proof method, by decide, means the computer evaluates both sides and confirms equality, a mechanical check with no hidden assumptions.

In Recognition Science, this declaration is one of many similar theorems in a chunk of the library. The chunk's docstring says m2Num = 8·explicitZ, and the file contains dozens of theorems, each for a different set of six indices, each proved by the same direct computation. Together they form a table of verified identities. This particular one, e_130001, is the first in its chunk, covering the index set 1, 3, 0, 0, 0, 1.

What the declaration does not claim is just as important. It does not assert anything about the physical meaning of m2Num or explicitZ. It does not say that the factor eight has any special significance. It does not claim that the identity holds for all indices, only for this one specific set. It does not establish any connection to the broader Recognition Science framework, such as the forcing chain that derives constants or dimensions. The theorem is a single, isolated, machine-checked numerical fact, useful as a building block but carrying no interpretation on its own.

theorem e_133333 : m2Num 1 3 3 3 3 3 = 8 * explicitZ 1 3 3 3 3 3 := by decide

theorem e_133333 : m2Num 1 3 3 3 3 3 = 8 * explicitZ 1 3 3 3 3 3 := by decide

What this page does not claim

The declaration does not assign any physical meaning to m2Num or explicitZ. The declaration does not claim the identity holds for any index set other than 1, 3, 0, 0, 0, 1. The declaration does not connect to the framework's forcing chain or derived constants.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk07.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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