Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk07 E 130003

The chunk theorem

A machine-checked library of formal theorems contains a file that verifies a long list of arithmetic identities. Each identity compares two functions, m2Num and explicitZ, at a specific six-digit input. The declaration e_130003 is the name of one entry in that list, and it states that at the input (1,3,0,0,0,3), the value of m2Num equals eight times the value of explicitZ.

The proof is a direct computation, written in the library as "by decide". This means the computer checks the equality by evaluating both sides and confirming they match. The declaration does not introduce a new physical law, does not define a new quantity, and does not prove a general theorem about gravity. It is a single, concrete arithmetic fact that the larger calculation relies on.

The file's name places it in a section of the library dealing with an exact midpoint identity in a four-dimensional gravity analysis. The identities are organized into chunks, and this one is chunk 7. The purpose of these chunks is to break a large verification into small, checkable pieces. Each chunk contains many such declarations, each one a separate arithmetic equality.

What e_130003 establishes is narrow and precise. It confirms that for this one input, the two functions stand in the stated eightfold relation. This is a proved theorem in the library, meaning the equality is checked by the machine and accepted as true. The declaration carries no claim about the meaning of the functions, no claim about physics beyond the arithmetic, and no claim that other inputs behave similarly.

The value of this declaration is in its role as a building block. Large formal proofs are constructed from thousands of small steps like this one. Each step is verified, and the whole chain is trusted because each link holds. This declaration is one such link, and its contribution is to make the larger calculation complete.

theorem e_133333 : m2Num 1 3 3 3 3 3 = 8 * explicitZ 1 3 3 3 3 3 := by decide

theorem e_133333 : m2Num 1 3 3 3 3 3 = 8 * explicitZ 1 3 3 3 3 3 := by decide

What this page does not claim

This declaration does not establish any physical law or property of gravity. This declaration does not prove that the identity holds for any input other than (1,3,0,0,0,3). This declaration does not define the functions m2Num or explicitZ.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk07.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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