Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk14 E 320000

A verified arithmetic identity

In the Recognition Science framework, the declaration e_320000 is a theorem about a specific arithmetic calculation. It states that a quantity called m2Num, evaluated at a particular six-number coordinate (3, 2, 3, 2, 0, 0), equals eight times another quantity called explicitZ at the same coordinate. The proof is a direct computation, marked by the Lean keyword decide, meaning the kernel checks the equality by evaluating both sides and confirming they match.

This declaration belongs to a larger collection: a set of 256 such identities, each covering a different coordinate combination, with the first coordinate fixed at 3 and the second at 2. The name "chunk 14" refers to one batch of these theorems in the machine-checked library. The library is a collection of formal theorems whose proofs are verified by a computer, leaving no room for human error in the arithmetic. The identity itself is a small piece of a larger effort to verify a gravity-related calculation called the Regge exact midpoint M2 TT identity in four dimensions.

What the declaration does not claim is broader significance. It does not assert that the gravity identity holds in general; it only verifies one numerical instance. It does not derive the identity from physical principles, nor does it interpret what m2Num or explicitZ mean physically. The theorem is a computational check, not a physical law. It also does not claim that the calculation is correct in the sense of matching experiment; it only confirms internal consistency between two defined quantities.

The value of such a declaration is in what it enables. A machine-checked library can build large proofs from many small verified steps. Each e_320000-style theorem is a brick. The reader can trust that the arithmetic is right, but the meaning of the calculation, its connection to gravity, and its physical relevance remain separate questions that this declaration does not address.

theorem e_323200 : m2Num 3 2 3 2 0 0 = 8 * explicitZ 3 2 3 2 0 0 := by decide

theorem e_323200 : m2Num 3 2 3 2 0 0 = 8 * explicitZ 3 2 3 2 0 0 := by decide

theorem e_323200 : m2Num 3 2 3 2 0 0 = 8 * explicitZ 3 2 3 2 0 0 := by decide

What this page does not claim

The declaration does not prove the gravity identity in general, only one numerical instance. The declaration does not assign physical meaning to the quantities m2Num or explicitZ. The declaration does not claim the calculation matches experimental measurement.

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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