Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk02 E 020002

A verified arithmetic identity

The declaration e_020002 is one entry in a large collection of machine-checked arithmetic facts. Each fact states that a particular numerical expression, called m2Num, equals eight times another expression, called explicitZ, for a specific set of six index values. The proof is a direct computation, verified by the machine-checked library of formal theorems, with no steps left to human judgment.

In plain terms, this is a bookkeeping check. The expressions m2Num and explicitZ are defined elsewhere in the framework's gravity analysis; this declaration confirms that for one particular combination of indices, the two quantities match exactly. The indices, such as 0 2 3 3 3 3, label a specific case within a larger grid of possibilities. The theorem e_023333, for instance, states that m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3, and the declaration e_020002 belongs to this same family of checks.

What this declaration does not claim is broader significance. It does not assert that the identity holds for all index values, nor does it explain what m2Num or explicitZ physically represent. It does not derive any gravitational law or connect to the framework's larger results about dimensions or constants. The proof is a single verified arithmetic step, not a physical statement. Its role is to ensure that one piece of a larger calculation is internally consistent, nothing more.

theorem e_023333 : m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3 := by decide

theorem e_023333 : m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3 := by decide

theorem e_023333 : m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3 := by decide

What this page does not claim

The declaration does not prove the identity for all index values, only for the specific case it names. The declaration does not state what m2Num or explicitZ physically mean. The declaration does not derive any gravitational law or connect to the framework's larger results.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk02.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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: