Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk14 E 320001

A numerical identity

The declaration e_320001 is a small, exact statement in a machine-checked library of formal theorems. It asserts that for a particular set of six indices, the value of a function called m2Num equals eight times the value of another function called explicitZ. The proof is a direct computation, written as by decide, which means the computer checked the arithmetic itself and found the equality true. This is not a general law or a new physical principle; it is a single verified instance within a larger framework.

In plain terms, the statement is like checking that a specific entry in a large table of numbers is correct. The table here concerns a quantity named m2Num, which appears in the framework's analysis of gravity. The indices, such as 3 2 3 3 3 3, label a particular position in that table. The theorem confirms that at that position, the value is exactly eight times the corresponding value in a second table, explicitZ. The factor of eight is a fixed relationship that holds for this entry and, according to the surrounding library, for many other entries in the same chunk of the proof.

What the declaration does not claim is equally important. It does not say what m2Num or explicitZ mean physically. It does not assert that gravity works this way in the world. It only establishes a numerical equality between two formally defined functions at one specific point. The broader significance, if any, comes from the context of the library: this identity is part of a chain of theorems that the framework uses to build its account of gravity. But this single declaration, taken alone, is just a verified arithmetic fact.

The practical consequence is reliability. Because the equality is machine-checked, a reader can trust that the arithmetic is correct without redoing it by hand. This is the kind of small, certain step that larger proofs are built from. It does not, by itself, prove anything about the physical world, but it provides a solid foundation for the framework's larger claims, which must stand on many such verified steps.

theorem e_323333 : m2Num 3 2 3 3 3 3 = 8 * explicitZ 3 2 3 3 3 3 := by decide

theorem e_323333 : m2Num 3 2 3 3 3 3 = 8 * explicitZ 3 2 3 3 3 3 := by decide

What this page does not claim

The declaration does not establish any physical law or empirical fact about gravity. The declaration does not define the functions m2Num or explicitZ. The declaration does not prove that the equality holds for any other set of indices.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk14.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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