Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk09

The 256-point check

Regge calculus is a way of doing general relativity without smooth geometry. Instead of a continuous spacetime, it uses a grid of flat pieces, like a geodesic dome approximating a sphere. The theory of Regge calculus was introduced by Tullio Regge in 1961, and it is the standard discretization used in numerical relativity and quantum gravity. The module named in the question is a small part of a much larger machine-checked library of formal theorems; it is one chunk of a computation that verifies an identity in this discrete setting.

The identity in question relates two quantities. On one side is m2Num, a number computed from the discrete geometry of a Regge grid. On the other side is 8 times explicitZ, a reference value. The chunk proves that for a specific set of 256 index combinations, these two sides are equal. Each theorem in the chunk, such as e_213333, states that m2Num 2 1 3 3 3 3 = 8 * explicitZ 2 1 3 3 3 3, and the proof is by decide, meaning a computer program checks the equality by direct calculation. The indices are the coordinates of the grid points; the chunk covers a block of the full index space.

In Recognition Science, this chunk is part of a larger effort to verify the consistency of its model of gravity. The framework derives physical constants and structures from a single cost function, and it treats conventional physics as itself RS-derived. The machine-checked library of formal theorems is the tool that audits these derivations. This chunk is a routine but necessary step: it confirms that the numerical values used in the gravity analysis match the explicit reference values, at the resolution of the grid. The name says what it does: it is the ninth chunk of a numerical check for the midpoint m2 identity in four dimensions.

What the chunk establishes, in plain language, is that a specific arithmetic identity holds at 256 points. It does not establish the identity for all points, and it does not establish any physical law. It is a building block, the kind of check that a large proof needs many of. The value of this chunk is not in any single equality, but in the fact that it is one more piece of the whole verified. The reader can now see that the framework's gravity analysis rests on a foundation of checked arithmetic, not on unexamined numerical assumptions.

theorem e_213333 : m2Num 2 1 3 3 3 3 = 8 * explicitZ 2 1 3 3 3 3 := by decide

What this page does not claim

This chunk does not prove the identity for all indices, only for the 256 in its range. This chunk does not establish any physical law or the correctness of Regge calculus as a theory. This chunk is not a derivation of the fine-structure constant or any other RS constant.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk09.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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