Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk04 E 100011

A single verified arithmetic identity

In the Recognition Science framework's machine-checked library of formal theorems, the declaration e_100011 is one entry in a large table of verified arithmetic identities. The library is a collection of mathematical statements whose proofs have been checked by a computer kernel, so each entry is a theorem: it states a precise equality and carries a proof that the equality holds. The specific statement is that a certain numerical function, written m2Num, returns a value exactly eight times another function, written explicitZ, when both are given the six input digits 1, 0, 0, 0, 1, 1. In symbols, the theorem reads m2Num 1 0 0 0 1 1 = 8 * explicitZ 1 0 0 0 1 1.

This is a computational identity, not a physical law. The function m2Num and the constant explicitZ are defined elsewhere in the framework's gravity analysis files, where they appear in the study of a discrete model of spacetime called a Regge lattice. The declaration itself does not explain what those functions mean physically; it only certifies that, for this one combination of inputs, the arithmetic relationship holds. The proof is by direct computation, which the kernel checks step by step, so the theorem is reliable within the framework's formal system.

The declaration is one of hundreds of similar entries in the same file, each covering a different six-digit input combination. Together they form a table of identities that the framework's developers use as building blocks for larger proofs about the Regge model. The single entry e_100011 does not, by itself, establish any property of gravity, any geometric fact, or any connection to measured physical constants. It is a verified arithmetic fact, nothing more and nothing less.

What the declaration does not claim is as important as what it proves. It does not claim that the equality holds for all inputs, only for the specific six digits listed. It does not claim that m2Num or explicitZ correspond to measurable quantities in the real world. It does not claim that the Regge model is correct or that the framework's approach to gravity is validated. Those are larger questions that the framework addresses elsewhere, if at all, and this single theorem is silent on all of them.

For a reader encountering the framework for the first time, the value of this declaration is as a concrete example of how the library works. It shows that the framework's claims are built from small, machine-verified steps, each one exact and each one limited in scope. The honesty of the framework lies in this precision: the theorem says exactly what it proves, and no more.

theorem e_103333 : m2Num 1 0 3 3 3 3 = 8 * explicitZ 1 0 3 3 3 3 := by decide

theorem e_103333 : m2Num 1 0 3 3 3 3 = 8 * explicitZ 1 0 3 3 3 3 := by decide

What this page does not claim

The declaration does not claim the identity holds for any input other than 1 0 0 0 1 1. The declaration does not claim m2Num or explicitZ correspond to measurable physical quantities. The declaration does not claim the Regge model is correct or that the framework's gravity approach is validated.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk04.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: