Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk10 E 220013

A verified arithmetic identity

In numerical analysis, a table of computed values is only as trustworthy as the arithmetic that fills it. The declaration e_220013 is one cell in such a table: it states that a quantity called m2Num, evaluated at the six indices 2,2,0,0,1,3, equals eight times a reference quantity called explicitZ at the same indices. The proof is a direct computation, written as by decide, meaning the machine checked every arithmetic step and found the equality exact.

The identity belongs to a family of results in a machine-checked library of formal theorems, part of the Recognition Science framework's treatment of gravity. The library builds a large array of these identities, each one verifying that a computed numerical term matches a scaled reference value. This particular declaration, e_220013, is one of many in a chunk covering index patterns that begin with 2,2. The framework's library proves each such identity by direct calculation, not by appeal to a physical principle.

What the declaration does not claim is just as important. It does not assert anything about the physical meaning of m2Num or explicitZ, nor does it state that gravity behaves in a particular way. It only certifies an arithmetic fact: for these six indices, the two expressions are equal up to the factor eight. The result carries no information about other index combinations, and it makes no statement about the framework's broader claims, such as the derivation of physical constants or the nature of space.

In Recognition Science, such declarations serve as building blocks. Each verified identity adds a small, certain tile to a larger mosaic of results. The value of e_220013 lies in its precision and its provenance: a reader can trust that the equality holds exactly, because a machine checked it. That trust does not extend beyond the arithmetic, and the declaration itself makes no promise about what the numbers mean.

theorem e_223333 : m2Num 2 2 3 3 3 3 = 8 * explicitZ 2 2 3 3 3 3 := by decide

What this page does not claim

This declaration does not claim any physical law or interpretation of the numbers. It does not claim the equality holds for any other set of indices. It does not claim the framework's broader gravity results are physically correct.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk10.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: