Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk01 E 010000

The identity

The declaration e_010000 is one line in a very large arithmetic table. The table compares two quantities for every combination of six indices, each index running from 0 to 3. The first quantity, written m2Num, is a number that arises in a gravity analysis. The second, explicitZ, is a separately defined reference value. The theorem states that for the specific index combination 0 1 0 0 0 0, the first quantity equals exactly eight times the second: m2Num 0 1 0 0 0 0 = 8 * explicitZ 0 1 0 0 0 0.

The proof is a computation. The Lean kernel checks the equality by direct evaluation, a method called decide. This means the statement is not an assumption or a conjecture; it is a proved theorem in the machine-checked library of formal theorems. The surrounding file contains hundreds of sibling theorems, each verifying the same eightfold relationship for a different index combination.

In Recognition Science, this is part of a larger forcing chain. The framework derives constants and structures from a single cost function, and this theorem checks a numerical consistency within that derivation. The identity itself is purely arithmetic: it says two defined expressions agree. It does not assert that gravity is quantized, that four dimensions are physical, or that the index values correspond to measurable spacetime coordinates.

The value of this declaration is granular verification. A large-scale derivation can hide errors in bulk; this theorem pins down one specific cell of the table. It is a building block, not a standalone physical law. A reader should understand it as a checked computation that supports the framework's internal consistency, not as evidence that any particular physical prediction is correct.

theorem e_013333 : m2Num 0 1 3 3 3 3 = 8 * explicitZ 0 1 3 3 3 3 := by decide

theorem e_013333 : m2Num 0 1 3 3 3 3 = 8 * explicitZ 0 1 3 3 3 3 := by decide

What this page does not claim

This theorem does not assert any physical law about gravity or spacetime. It does not claim that the eightfold relationship holds for index combinations outside the verified set. It does not establish that the quantities m2Num or explicitZ correspond to measurable physical observables.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk01.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: