Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk13 E 310003

A numerical identity

The declaration e_310003 is a theorem in the framework's machine-checked library of formal theorems. It states a numerical identity: for a specific set of six indices, the value of a function called m2Num equals eight times the value of another function called explicitZ. The proof is by `decide`, which means the computer algebraically evaluates both sides and finds them equal. This is a fully verified claim, not an approximation or a conjecture.

The theorem is one entry in a large table. The library contains hundreds of similar theorems, each for a different combination of six indices, all asserting the same pattern: m2Num equals eight times explicitZ. The declaration e_310003 is the particular entry for the index combination (3,1,0,0,0,3). The docstring notes this is part of "chunk 13 (256 kernel decides)", meaning this block of theorems was checked by direct computation in the kernel.

In Recognition Science, this identity is part of a broader effort to verify structural relationships in gravity analysis. The framework models physical structure through a discrete ledger of recognition events, and these numerical identities are checks that the formal definitions behave consistently. The theorem itself does not derive any physical law; it verifies that two defined functions agree at a specific point.

The practical significance is one of confidence and completeness. Each such theorem is a small, machine-checked confirmation that the framework's definitions are internally consistent. The declaration e_310003 adds one more data point to a pattern that holds across hundreds of index combinations, strengthening the evidence that the underlying definitions are coherent.

theorem e_313333 : m2Num 3 1 3 3 3 3 = 8 * explicitZ 3 1 3 3 3 3 := by decide

theorem e_313333 : m2Num 3 1 3 3 3 3 = 8 * explicitZ 3 1 3 3 3 3 := by decide

What this page does not claim

The theorem does not derive any physical law or gravitational prediction. The identity does not establish that the pattern holds for all index combinations, only for the verified ones. The declaration does not define what m2Num or explicitZ mean physically.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk13.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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