Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk05 E 110002

A numerical identity in the gravity analysis

The declaration e_110002 belongs to a family of theorems in a machine-checked library of formal theorems. Each theorem in this family states that for a particular choice of six indices, a quantity called m2Num equals eight times a quantity called explicitZ. The proof of each such statement is a direct computation, recorded by the keyword "by decide", which means the computer checked the arithmetic by evaluating both sides. The declaration e_110002 itself is one instance of this pattern, for the indices 1 1 3 3 1 2, and it establishes that m2Num 1 1 3 3 1 2 = 8 * explicitZ 1 1 3 3 1 2.

In plain language, the declaration verifies a specific numerical relationship inside a larger table. The table appears in a section of the library concerned with an exact midpoint analysis in a theory of gravity. The names m2Num and explicitZ are defined elsewhere in the library; this declaration does not define them, it only states and proves the equality for the chosen indices. The theorem does not interpret the physical meaning of the numbers, nor does it connect them to any measured quantity. It is a purely formal, computational result: for this one entry in the table, the two expressions agree.

The declaration does not claim that the equality holds for all indices, nor does it assert that the pattern continues beyond the listed cases. It does not derive the values of m2Num or explicitZ from first principles, and it does not explain why the factor of eight appears. The theorem is a single verified row in a larger computational ledger, a discrete record of events, and its role is to confirm that this particular arithmetic step is correct. What the declaration changes is the confidence in the table: a reader can rely on this one entry without recomputing it by hand.

theorem e_113312 : m2Num 1 1 3 3 1 2 = 8 * explicitZ 1 1 3 3 1 2 := by decide

What this page does not claim

The declaration does not prove the equality for all indices, only for the listed one. The declaration does not define m2Num or explicitZ. The declaration does not connect the numerical identity to any measured physical value.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk05.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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