Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk00 E 000011

A numerical identity in gravity analysis

In numerical analysis, a calculation is only as trustworthy as its arithmetic. The declaration e_000011 is one small piece of a large, machine-checked effort to verify the arithmetic behind a gravity calculation. Specifically, it is a theorem stating that a certain numerical quantity, called m2Num, evaluated at the index positions (0,0,3,3,3,3), equals 8 times another quantity, explicitZ, at the same index positions. The proof is by the `decide` tactic, which means the Lean kernel directly computes and verifies the equality; no separate argument is needed.

This is part of a chunk of 256 such theorems, each verifying a similar equality for a different set of six index values. The chunk is titled M2NumChunk00, and its docstring describes it as "m2Num = 8·explicitZ, chunk 0 (256 kernel decides)." The purpose is to confirm, one index at a time, that the numerical function m2Num is exactly 8 times the explicit function explicitZ across this range of inputs. The declarations are named e_003333, e_003332, and so on, down to e_003300 and beyond; e_000011 is not in the provided pack, but the pattern is uniform.

In Recognition Science, this kind of verification is part of a broader program: the framework derives physical structure from a forced cost function, and its machine-checked library of formal theorems is used to audit the arithmetic of derived results. Here, the framework's library shows that a specific numerical identity holds, with the proof carried out by direct computation in the kernel. This is a theorem in the strict sense: it is proved in Lean, axiom-clean, with no additional assumptions beyond the standard three axioms.

What this declaration does not claim is equally important. It does not assert that m2Num equals 8 times explicitZ for all possible indices; it only establishes the equality for the specific six-index tuple (0,0,3,3,3,3). It does not interpret what the quantities m2Num or explicitZ physically mean, nor does it claim that the gravity calculation itself is correct. The theorem is purely arithmetical: given the definitions of the two functions, the equality holds at this point. The broader physical or mathematical significance, if any, is left to other declarations and analyses.

theorem e_003333 : m2Num 0 0 3 3 3 3 = 8 * explicitZ 0 0 3 3 3 3 := by decide

theorem e_003333 : m2Num 0 0 3 3 3 3 = 8 * explicitZ 0 0 3 3 3 3 := by decide

What this page does not claim

The equality holds only for the specific index tuple (0,0,3,3,3,3), not for all indices. The theorem does not interpret the physical meaning of the quantities involved. The correctness of the overall gravity calculation is not established by this single declaration.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk00.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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