Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk02 E 020000

The arithmetic check

The declaration e_020000 is a theorem in the Recognition Science framework's machine-checked library of formal theorems. It states that the value of a function called m2Num, evaluated at the six indices 0, 2, 0, 0, 0, 0, equals eight times the value of another function called explicitZ at the same indices. In symbols: m2Num 0 2 0 0 0 0 = 8 * explicitZ 0 2 0 0 0 0. The proof is by the `decide` tactic, which means the computer checks the equality by direct computation on the concrete numbers.

The context shows this is part of a larger project: a file named ReggeExactMidpointM2TTIdentity4DM2NumChunk02.lean, which is one chunk of a verification of an identity involving Regge calculus, a discrete approximation to general relativity used in numerical simulations. The function m2Num appears to compute some numerical quantity from six indices, and explicitZ provides a reference value. The theorem establishes that for this particular combination of indices, the computed value is exactly eight times the reference.

The declaration does not claim to prove the full Regge identity, nor does it say anything about the physical meaning of m2Num or explicitZ. It does not assert that the equality holds for all indices; it is a single concrete instance, checked by computation. The broader identity, if it exists, would be a separate theorem. The declaration also does not claim that the factor of eight has any physical significance; it is simply the result of the computation for these specific inputs.

In plain terms, this is a bookkeeping step. The framework is building a large, machine-verified argument, and this theorem is one line in that ledger, confirming that a particular arithmetic entry is correct. What it changes is that a reader can trust this one numerical fact without manually recomputing it, and the larger project can build on it.

theorem e_023333 : m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3 := by decide

theorem e_023333 : m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3 := by decide

What this page does not claim

The theorem does not prove the full Regge identity. The theorem does not assign physical meaning to m2Num or explicitZ. The theorem does not claim the equality holds for all index combinations.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk02.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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