Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk12 E 300011

A numerical check in the gravity ledger

The declaration e_300011 is one small entry in a large bookkeeping exercise. The Recognition Science framework keeps a discrete record of events, a ledger, and this particular statement checks one cell of a table that arises in a gravity calculation. The table records values called m2Num, which come from a formula involving an explicit function named explicitZ. The declaration proves that for a specific set of six indices, the value of m2Num equals eight times the value of explicitZ.

The proof is a direct computation. The statement is tagged as a theorem in the machine-checked library of formal theorems, and its proof is the single word "decide", meaning the computer evaluates both sides of the equation and finds them identical. The indices in question are 3, 0, 3, 3, 0, 0, and the equality is m2Num 3 0 3 3 0 0 = 8 * explicitZ 3 0 3 3 0 0. This is not a general law; it is a specific numerical identity for one combination of inputs.

The declaration belongs to a chunk of 256 similar statements, each checking a different set of indices. The chunk is named chunk 12, and the surrounding module name refers to an exact midpoint calculation in a four-dimensional gravity analysis. The purpose of the whole collection is to verify that the m2Num function, which is defined by a separate formula, agrees with the explicitZ function scaled by a factor of eight across a range of inputs. Each theorem is independent, and each is checked by the same mechanical procedure.

What the declaration does not claim is just as precise as what it does. It does not state that the equality holds for all indices; it states it for one specific sextuple. It does not derive the formula for m2Num or explicitZ; it assumes those definitions and checks a consequence. It does not connect this numerical identity to any physical measurement, any empirical prediction, or any other theorem in the framework. The statement is a local arithmetic fact, verified by computation, and its significance within the larger gravity analysis is a matter for the surrounding development, not for this single declaration.

theorem e_303300 : m2Num 3 0 3 3 0 0 = 8 * explicitZ 3 0 3 3 0 0 := by decide

What this page does not claim

The equality does not hold for all indices, only for the specific sextuple checked. The declaration does not derive the formulas for m2Num or explicitZ. No physical measurement or empirical prediction is involved in this statement.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk12.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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