Encyclopedia Gravity Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk05 E 110013

ARTICLE 1 claim 1 theorem

Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk05 E 110013

A machine-checked proof verifies that a specific six-index expression in a gravity calculation equals exactly eight times a reference value, not an approximation.

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The exact midpoint identity

The declaration e_110013 is a single verified step inside a larger calculation in the Recognition Science framework's machine-checked library of formal theorems. The statement it proves is a concrete numerical identity: for the index tuple (1,1,3,3,3,2), the quantity written m2Num equals exactly 8 times the quantity written explicitZ. The proof is by decide, meaning the computer checks the equality by direct computation, with no hidden assumptions and no hand-written argument.

The identity belongs to a family of similar statements, each covering one six-index combination, and this particular one is part of chunk 5 of the calculation. The name of the containing module, ReggeExactMidpointM2TTIdentity4D, indicates the context: a four-dimensional setting where a midpoint evaluation in a Regge-style discrete gravity analysis is being checked. The 'exact' in the name is the point. The result is not a numerical approximation or a limiting statement; it is an equality that holds precisely, and the machine has verified it.

In Recognition Science, this kind of declaration is a building block. The framework's library accumulates such verified identities so that later results can rely on them without re-checking. This particular identity does not by itself establish any physical law or derive a constant. It is a computational fact about the symbols m2Num and explicitZ as defined in the library, and it is true by direct evaluation.

What e_110013 does not claim is equally clear. It does not state that the identity holds for all index tuples, only for the specific one named. It does not interpret m2Num or explicitZ physically, and it does not say that this equality has any bearing on the empirical content of gravity. The declaration is a lemma, not a theory of gravity, and it carries no claim about measurement or experiment.

THEOREM e_113332 · IndisputableMonolith/Gravity/Analysis/ReggeExactMidpointM2TTIdentity4DM2NumChunk05.lean
e_113332 · IndisputableMonolith/Gravity/Analysis/ReggeExactMidpointM2TTIdentity4DM2NumChunk05.lean:271 
theorem e_113332 : m2Num 1 1 3 3 3 2 = 8 * explicitZ 1 1 3 3 3 2 := by decide

What this page does not claim

This declaration does not establish a physical law or derive a constant. This declaration does not state that the identity holds for any index tuple other than the one named. This declaration does not interpret m2Num or explicitZ in physical terms.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk05.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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