Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk11

A numerical ledger for gravity

Regge calculus is a way to study gravity without smooth geometry. Instead of a continuous curved spacetime, it builds space from flat pieces, like approximating a sphere with many small triangles. The curvature lives at the joints, where the pieces meet. This chunk of a larger verification effort checks a specific set of numerical identities in that discrete setting.

The identities take a simple form. For each of 40,000 combinations of six indices, the chunk proves that a quantity called m2Num, a number computed from the discrete geometry, equals 8 times another quantity, explicitZ, a separately defined reference value. The theorem statement for one example reads: m2Num 2 3 3 3 3 3 = 8 * explicitZ 2 3 3 3 3 3. The proof for each identity is the single word "decide", meaning the computer checks the arithmetic directly.

This is a bookkeeping exercise, not a new physical law. The chunk does not derive gravity from first principles. It verifies that a proposed numerical scheme, the m2Num values, is consistent with a chosen baseline, the explicitZ values, up to a fixed factor of 8. The factor is a scaling choice built into the definitions.

In Recognition Science, this kind of check plays a supporting role. The framework's core theorems force the existence of a recognition cycle and three spatial dimensions, but turning those abstract results into concrete numerical predictions requires many small, exact computations. This chunk is one such computation, a brick in a larger wall. It establishes that a particular discrete model of curvature, at a midpoint of its parameter space, matches its own reference standard exactly.

The practical consequence is confidence. A large set of arithmetic facts has been checked by machine, not by hand. Any later result that relies on these 40,000 identities can cite them as proved. The chunk does not say what gravity is, but it certifies that this part of the numerical machinery is sound.

theorem e_233333 : m2Num 2 3 3 3 3 3 = 8 * explicitZ 2 3 3 3 3 3 := by decide

theorem e_233333 : m2Num 2 3 3 3 3 3 = 8 * explicitZ 2 3 3 3 3 3 := by decide

What this page does not claim

This chunk does not derive gravity from Recognition Science first principles. The factor of 8 is not derived; it is a scaling choice in the definitions. The chunk does not make a physical prediction about measurable gravitational phenomena.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk11.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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