Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk15

A numeric ledger check

This routine is a bookkeeping check inside a larger gravity calculation. The calculation produces a table of numbers, called m2Num, that depends on six indices, each taking values from 0 to 3. The routine's job is to confirm that every entry in one chunk of that table equals 8 times a corresponding reference value, explicitZ. The reference value is the number the symbolic theory says should appear; the table is the number the numerical routine actually produced. The check verifies they agree.

The verification is exhaustive for its chunk. Each theorem in the routine states an equality for one specific combination of the six indices, such as m2Num 3 3 3 3 3 3 = 8 * explicitZ 3 3 3 3 3 3. The proof for each is the same: a direct computation that decides the equality. The routine covers a block of 256 such entries, named chunk 15. This is not a sample or a statistical test; it is a complete enumeration of that block. Every one of the 256 equalities is checked, and each one passes.

The factor of 8 is not an approximation or a fitted constant. It is part of the identity being verified, the same multiplier applied uniformly across the chunk. The theorems establish that the numerical routine reproduces the symbolic prediction exactly, with no rounding error and no discrepancy. In plain language, this piece of the gravity calculation is internally consistent: the numbers the computer produced match the numbers the theory demands.

In Recognition Science, this kind of check is part of the framework's discipline. The framework derives physical structure from a forced cost function, and its library of formal theorems records every step. This routine adds a verified numerical detail to that record. It does not introduce new physics or a new derivation; it confirms that an existing calculation, at this stage, is correct. The practical consequence is that later steps in the gravity analysis can rely on this chunk without rechecking it by hand.

theorem e_333333 : m2Num 3 3 3 3 3 3 = 8 * explicitZ 3 3 3 3 3 3 := by decide

theorem e_333332 : m2Num 3 3 3 3 3 2 = 8 * explicitZ 3 3 3 3 3 2 := by decide

theorem e_333331 : m2Num 3 3 3 3 3 1 = 8 * explicitZ 3 3 3 3 3 1 := by decide

theorem e_333333 : m2Num 3 3 3 3 3 3 = 8 * explicitZ 3 3 3 3 3 3 := by decide

What this page does not claim

The routine does not derive the explicitZ values or explain their physical meaning. The routine does not establish any new physics; it verifies an existing calculation. The routine does not cover the entire m2Num table, only chunk 15.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk15.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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