Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk10 E 220003

A numerical identity in the gravity analysis

The declaration e_220003 belongs to a family of theorems in the Recognition Science framework's machine-checked library of formal theorems. Each theorem in this family states that a quantity called m2Num, evaluated at a particular set of six indices, equals eight times another quantity called explicitZ at the same indices. The proof of each theorem is a direct computation, marked by the word "decide", meaning the equality holds by evaluating the definitions on both sides.

In plain terms, the declaration establishes a numerical identity: for the specific index combination 2 2 0 0 0 3, the value of m2Num is exactly eight times the value of explicitZ. This is not a general law or a physical principle. It is a concrete, verified arithmetic fact about two functions defined within the framework's gravity analysis, specifically in the file ReggeExactMidpointM2TTIdentity4DM2NumChunk10.lean.

The broader context is a series of such identities, each covering a different index combination. The file contains dozens of similar theorems, each asserting the same eightfold relationship for its own six indices. The declaration e_220003 is one entry in this list, confirming the relationship for its particular case. The computation is exact and kernel-checked, meaning a proof assistant verified the arithmetic step by step.

What the declaration does not claim is equally important. It does not assert that this identity holds for all indices, nor does it explain why the factor eight appears. It does not connect m2Num or explicitZ to any measured physical quantity, nor does it derive a force law or a constant of nature. The theorem is a local, computational fact within a larger formal development; its significance depends on the definitions of m2Num and explicitZ, which the pack does not provide in detail.

theorem e_223203 : m2Num 2 2 3 2 0 3 = 8 * explicitZ 2 2 3 2 0 3 := by decide

theorem e_223203 : m2Num 2 2 3 2 0 3 = 8 * explicitZ 2 2 3 2 0 3 := by decide

What this page does not claim

The declaration does not establish a general law valid for all index combinations. The declaration does not connect m2Num or explicitZ to any measured physical quantity. The declaration does not explain the origin or significance of the factor eight.

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

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