Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk10 E 220011

A single verified arithmetic fact

The declaration e_220011 is a single, narrow arithmetic statement inside a much larger formal project. It says that a particular number, labeled m2Num 2 2 0 0 1 1, equals eight times another number, labeled explicitZ 2 2 0 0 1 1. The proof is by direct computation, the kind of step a computer can check exhaustively. It is a small fact, not a law of nature.

The context matters. This declaration lives in a file about something called the Regge exact midpoint, which is part of a framework's exploration of gravity. The names suggest a discrete model of spacetime, where numbers are attached to small pieces of a grid. But the declaration itself does not explain what m2Num or explicitZ mean. It only asserts a numerical relationship between them for one specific set of six indices: 2, 2, 0, 0, 1, 1.

What the declaration does establish is that, within the definitions of that file, the two quantities are related by a factor of eight. This is a theorem in the machine-checked library of formal theorems. The proof method, by decide, means the computer evaluated both sides and found them equal. It is a verified computation, not a guess or an approximation.

What it does not claim is far more important. It does not say that gravity works this way, that spacetime is discrete, or that the number eight has physical meaning. It does not derive any equation of motion, any force law, or any observable prediction. It is not a measurement and it is not a hypothesis about the universe. It is one row in a table, checked and filed.

The honest summary is this: e_220011 proves that a specific arithmetic identity holds in a specific formal system. That is all. The reader should not take from it any statement about physical reality, because the declaration itself makes none.

theorem e_223333 : m2Num 2 2 3 3 3 3 = 8 * explicitZ 2 2 3 3 3 3 := by decide

theorem e_223332 : m2Num 2 2 3 3 3 2 = 8 * explicitZ 2 2 3 3 3 2 := by decide

theorem e_223331 : m2Num 2 2 3 3 3 1 = 8 * explicitZ 2 2 3 3 3 1 := by decide

theorem e_223330 : m2Num 2 2 3 3 3 0 = 8 * explicitZ 2 2 3 3 3 0 := by decide

What this page does not claim

This declaration does not claim that spacetime is discrete or that gravity is quantized. This declaration does not derive any physical law, equation of motion, or observable prediction. This declaration does not assign physical meaning to the number eight or to the indices 2, 2, 0, 0, 1, 1.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk10.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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