Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk15 E 330012

A single arithmetic check

The declaration e_330012 is a single, fully verified arithmetic fact. It states that for one specific combination of six indices, the value of a function called m2Num equals eight times the value of another function called explicitZ. The indices in this case are 3, 3, 0, 0, 1, and 2. The proof is not a long argument; it is a direct computation that the machine checks by deciding the equality. This is the mathematical equivalent of confirming that 2 + 2 = 4, but for a much more elaborate expression.

The context is a project in Recognition Science that studies gravity through a discrete, ledger-like model. In this model, space and time are not continuous but are built from a finite grid of points. The functions m2Num and explicitZ are two different ways to compute a quantity associated with a small piece of this grid. The identity being tested claims that these two methods always agree, and e_330012 confirms that agreement for this one particular case. The declaration is part of a larger file that checks many such cases, each with different indices, and each verification is a separate theorem.

What e_330012 does not claim is broader than what it does. It does not prove that the identity holds for all possible index combinations. It only verifies this one instance. It does not explain what m2Num or explicitZ physically represent, nor does it derive them from more basic principles. The declaration is a check, not a theory. It is a building block in a larger verification effort, not a standalone result about the nature of gravity.

The practical significance is that such checks build confidence. When a proposed identity is tested across many individual cases and every single one passes, the evidence for the general statement grows. This particular declaration is one small piece of that accumulating evidence. It is a concrete, machine-verified fact that can be relied upon, even if the full theory behind it remains a subject of ongoing work.

theorem e_333312 : m2Num 3 3 3 3 1 2 = 8 * explicitZ 3 3 3 3 1 2 := by decide

theorem e_333312 : m2Num 3 3 3 3 1 2 = 8 * explicitZ 3 3 3 3 1 2 := by decide

What this page does not claim

This declaration does not prove the identity holds for all index combinations. This declaration does not provide a physical interpretation of the functions involved. This declaration does not derive the functions from more fundamental principles.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk15.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: