Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk01 E 010001

A numerical identity

In the Recognition Science framework, a ledger is a discrete record of events, and the framework's library is a machine-checked collection of formal theorems. The declaration e_010001 is one entry in a long list of theorems that check a numerical identity. The identity states that a certain function, called m2Num, when evaluated at a specific set of six indices, equals eight times another function, explicitZ, evaluated at the same indices. The proof is by a computer procedure that decides the equality by direct calculation, not by a symbolic derivation.

The specific indices in e_010001 are not shown in the available record, but the surrounding entries show the pattern. For example, the theorem e_013333 states that m2Num 0 1 3 3 3 3 equals 8 times explicitZ 0 1 3 3 3 3, and e_013332 states the same for indices 0 1 3 3 3 2. Each theorem in the chunk covers one combination of six indices, and each is proved by the same direct calculation. The collection covers many combinations, forming a block of verified arithmetic facts.

The declaration does not establish any physical claim about gravity, despite the name of the file. It does not prove that gravity exists, that a particular equation of motion holds, or that any measured value matches a prediction. The identity is a purely formal statement about two defined functions. The framework's broader claims about gravity, such as the forcing of three spatial dimensions, rest on other theorems in the library, not on this numerical chunk.

What the declaration does establish is that a specific arithmetic relationship holds, and that the relationship was checked by a kernel-verified procedure. This is a small but solid piece of the framework's larger project: building a body of results where every computational step is audited. The reader can take from this entry one concrete fact: for the indices covered, the equality m2Num = 8 * explicitZ holds, and the proof is a direct calculation.

theorem e_013333 : m2Num 0 1 3 3 3 3 = 8 * explicitZ 0 1 3 3 3 3 := by decide

theorem e_013333 : m2Num 0 1 3 3 3 3 = 8 * explicitZ 0 1 3 3 3 3 := by decide

What this page does not claim

The declaration does not establish any physical law about gravity. The declaration does not prove that any measured value matches a framework prediction. The declaration does not show that the identity holds for indices outside the verified chunk.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk01.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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