Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk05 E 110010

A numerical identity, verified

The declaration e_110010 is a single verified arithmetic fact inside a larger verification project. It states that a quantity called m2Num, evaluated at a specific six-digit index, equals eight times another quantity called explicitZ at the same index. The proof is a direct computation, marked by the word "decide", meaning the computer checked the arithmetic itself. This is not a new physical law; it is a bookkeeping check that one number in a table matches the pattern the table is supposed to follow.

The context is a study of gravity in four dimensions, using a framework called Recognition Science. The framework models physical structure through a ledger, a discrete record of recognition events, and derives constants and dimensions from a forced cost function. Here, the work concerns the Regge exact midpoint, a specific way of discretizing spacetime, and an identity involving the quantity m2Num. The declaration e_110010 is one of hundreds of similar theorems, each confirming that for a particular choice of indices, the relation m2Num = 8 * explicitZ holds.

The index 1 1 0 0 1 0 is one point in a six-dimensional grid of possibilities. Each theorem in the chunk covers one such point, and together they build a complete table. The number 256 appears in the docstring as the size of the decision, meaning the computation covers a finite set of cases. The declaration e_110010 is the specific case at that index, and its proof is a direct check, not a derivation from deeper principles.

What the declaration does not claim is as important as what it does. It does not prove the gravitational identity itself; it only verifies one numerical instance of it. It does not establish the framework's axioms or the derivation of the cost function. It does not say anything about the physical meaning of m2Num or explicitZ beyond their role in this computation. The declaration is a piece of the verification machinery, not a standalone result about gravity.

theorem e_113233 : m2Num 1 1 3 2 3 3 = 8 * explicitZ 1 1 3 2 3 3 := by decide

theorem e_113233 : m2Num 1 1 3 2 3 3 = 8 * explicitZ 1 1 3 2 3 3 := by decide

What this page does not claim

The declaration does not prove the underlying gravitational identity, only one numerical instance of it. The declaration does not establish the Recognition Science framework's axioms or the derivation of its cost function. The declaration does not assign physical meaning to m2Num or explicitZ beyond their role in this computation.

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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