Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk14 E 320003

A numerical check in chunks

In numerical analysis, a large computation is often broken into many small pieces, each checked on its own. The declaration e_320003 is one such piece. It states that for a particular set of six indices, the value of a function called m2Num equals eight times the value of another function called explicitZ. The proof is a direct computation: the ledger, a discrete record of events, is checked entry by entry.

The theorem is one of dozens in a file that covers a grid of index combinations. Each theorem has a name like e_323233 or e_323232, and each states the same kind of equality for a different set of six indices. The file is part of a larger project on gravity, specifically on a quantity called m2 that appears in a four-dimensional analysis. The name Regge refers to a method for approximating curved spacetime with flat pieces, and the file checks that the computed m2 values match the explicit formula at the midpoint of each cell.

The proof method is "by decide," which means the computer checks the equality by evaluating both sides directly. This is a brute-force verification, not a symbolic derivation. It confirms that for these specific inputs, the two functions agree. It does not prove that they agree for all inputs, nor does it explain why the equality holds. It is a local check, not a global law.

In Recognition Science, this kind of check is part of a larger forcing chain that derives physical constants from a single cost function. The framework proves that any cost function satisfying five conditions must equal a specific form, and from that it derives the golden ratio, an eight-tick cycle, and three spatial dimensions. The gravity analysis is a separate, later step that applies these ideas to a concrete numerical problem. This declaration is a small verification within that application.

What this declaration does not claim is important. It does not claim that the equality holds for all indices, only for the one specific combination. It does not claim that the m2 function is physically meaningful, only that it matches the explicit formula at this point. It does not claim that the gravity analysis is complete or that it proves any new physics. It is a single data point, verified by brute force, in a much larger project.

The value of this check is that it catches errors early. If the m2 function had a bug, the equality would fail here, and the error would be found before the analysis proceeds. This is the role of such declarations: they are the building blocks of a reliable computation. Each one is small, but together they form a foundation that can be trusted.

A reader who wants to understand the full gravity analysis should look at the surrounding theorems and the definitions of m2Num and explicitZ. This declaration is a single brick in a wall, not the wall itself.

theorem e_323333 : m2Num 3 2 3 3 3 3 = 8 * explicitZ 3 2 3 3 3 3 := by decide

theorem e_323333 : m2Num 3 2 3 3 3 3 = 8 * explicitZ 3 2 3 3 3 3 := by decide

What this page does not claim

The equality holds for all index combinations, only for the one specified. The m2 function has physical significance beyond matching the explicit formula at this point. The gravity analysis is complete or proves new physics.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk14.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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