Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk05 E 110012

A numerical identity in the gravity analysis

The declaration e_110012 is one entry in a long list of computer-checked arithmetic facts. Each fact states that a certain function, called m2Num, equals eight times another function, called explicitZ, for a particular set of six input numbers. The inputs are combinations of 0, 1, 2, and 3. For example, one theorem in the same list proves that m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3. The proof is by decide, meaning the computer simply calculates both sides and confirms they are equal.

These identities appear in a file named ReggeExactMidpointM2TTIdentity4D, part of a larger gravity analysis. The names suggest the quantities relate to Regge calculus, a discrete approach to general relativity, and to a midpoint construction in four dimensions. The file's docstring notes that this is chunk 5, where a 256-case kernel decides the result. So the declaration is a building block in a systematic verification of many similar numerical equalities.

In Recognition Science, the framework uses a machine-checked library of formal theorems to build its results. This declaration is a small, concrete instance of that method: it does not prove a general law or a physical principle. It merely confirms one arithmetic relation among defined functions. The value of such checks is that they are exact and auditable, not that they carry physical meaning by themselves.

What e_110012 does not claim is important. It does not say that the identity holds for all inputs, only for the specific six numbers named. It does not interpret m2Num or explicitZ physically, and it does not connect them to any measured quantity or experimental prediction. The declaration is a formal arithmetic fact, not a statement about gravity, spacetime, or any observable effect.

theorem e_113333 : m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3 := by decide

theorem e_113333 : m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3 := by decide

theorem e_113333 : m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3 := by decide

What this page does not claim

The declaration does not prove the identity for all possible inputs. The declaration does not assign physical meaning to m2Num or explicitZ. The declaration does not connect to any measured gravitational quantity.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk05.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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