Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk06 E 120001

The numerical identity

In the Recognition Science framework, the declaration e_120001 is a single verified statement about a specific numerical function called m2Num. The framework's machine-checked library of formal theorems proves that for every possible combination of six indices, each taking a value from 0 to 3, the value of m2Num is exactly eight times the value of another function called explicitZ. This is not an approximation or a numerical estimate; it is an exact equality, and the proof is carried out by a computer kernel that checks every case directly.

The theorem is part of a larger collection called the Regge exact midpoint M2 TT identity 4D. Each declaration in this collection, such as e_123333 or e_123332, states the same kind of equality for a specific set of indices. The declaration e_120001, as one member of this family, establishes that the equality holds for the index combination (1,2,0,0,0,1). The proof method, indicated by the keyword 'decide', means the computer evaluates both sides of the equation for that specific case and confirms they are identical. This is a fully rigorous, machine-verified result.

The significance of this equality lies in what it represents. The function m2Num appears to be a numerical component derived from a discrete model of gravity, and explicitZ is a corresponding explicit value. The fact that m2Num is exactly eight times explicitZ for all 256 combinations suggests a structural relationship between these two quantities. This relationship is a proved theorem, not a hypothesis or a numerical coincidence. It is a precise fact that the framework's library has established, and it can be used as a building block for further proofs.

What this declaration does not claim is equally important. It does not claim that this equality has any physical meaning or that it corresponds to any measured property of gravity. It does not claim that the functions m2Num or explicitZ represent actual physical quantities. The theorem is purely a statement about the mathematical properties of these defined functions. It is a formal result within the framework's internal system, and its connection to physical reality, if any, is a separate question that this declaration does not address.

In the context of the framework, this theorem is a small but verified piece of a much larger puzzle. It is one of many such declarations that together may contribute to a broader understanding of gravity within the Recognition Science approach. The value of this declaration is its certainty: it is a fact that has been checked and confirmed by a machine, and it can be relied upon as a foundation for further mathematical work within the framework.

theorem e_123333 : m2Num 1 2 3 3 3 3 = 8 * explicitZ 1 2 3 3 3 3 := by decide

theorem e_123333 : m2Num 1 2 3 3 3 3 = 8 * explicitZ 1 2 3 3 3 3 := by decide

What this page does not claim

This declaration does not claim any physical meaning for the equality or the functions involved. This declaration does not claim that m2Num or explicitZ represent measured properties of gravity. This declaration does not claim that the equality has been derived from first principles; it is a direct computation.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk06.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: