Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk01 E 010013

A verified arithmetic identity

The declaration e_010013 is a single, machine-checked proof of an arithmetic identity. It states that for the index combination (0, 1, 3, 3, 3, 3), the value of a function called m2Num equals 8 times the value of another function called explicitZ. The proof is completed by the kernel's decision procedure, which means the computer verified the equality by direct computation, not by a chain of abstract reasoning.

This identity is one small piece of a much larger verification effort. The file containing this declaration is part of a series that checks 256 such identities, one for each possible combination of six indices. Each identity asserts the same relationship: m2Num equals 8 times explicitZ for that specific index set. The declaration e_010013 covers the case where the indices are 0, 1, 3, 3, 3, 3. The name of the file, ReggeExactMidpointM2TTIdentity4D, suggests this is part of a check on a four-dimensional calculation related to Regge calculus, a discrete approach to general relativity.

In Recognition Science, this declaration is a THEOREM. It is a proved statement in the framework's machine-checked library of formal theorems. The proof is axiom-clean, meaning it relies only on the standard rules of logic and computation, not on any special assumptions from the framework itself. The identity itself is a concrete, verified fact about the two functions at a particular point.

What this declaration does not claim is broader significance. It does not assert that the identity holds for all index combinations; that would be a separate, more general theorem. It does not explain what m2Num or explicitZ physically represent, nor does it interpret the 8 in the relationship. It is a single, verified data point in a larger proof structure. The meaning of the identity, its connection to gravity or to the framework's other results, is established by other declarations and theorems, not by this one.

theorem e_013333 : m2Num 0 1 3 3 3 3 = 8 * explicitZ 0 1 3 3 3 3 := by decide

theorem e_013333 : m2Num 0 1 3 3 3 3 = 8 * explicitZ 0 1 3 3 3 3 := by decide

theorem e_013333 : m2Num 0 1 3 3 3 3 = 8 * explicitZ 0 1 3 3 3 3 := by decide

What this page does not claim

The declaration does not prove the identity for all 256 index combinations, only for this one. The declaration does not interpret the physical or mathematical meaning of the functions involved. The declaration does not establish any connection to the broader Recognition Science framework's other results.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk01.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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