Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk09 E 210003

A machine-checked arithmetic fact

The declaration e_210003 is a small, machine-checked arithmetic fact. It states that a certain computed value, written m2Num 2 1 3 3 3 3, equals eight times another computed value, written explicitZ 2 1 3 3 3 3. The proof is by decide, meaning the computer simply evaluated both sides and confirmed they are equal. This is not a physical law or a geometric theorem; it is a bookkeeping check inside a much larger formal development.

To see what the numbers mean, imagine a grid of positions, each labeled by six coordinates. The function m2Num takes one such position and returns a number; explicitZ takes the same position and returns another number. The identity says that for this particular position, the first number is exactly eight times the second. The declaration is one of many similar statements in the same file, each covering a different position. Together they form a chunk of a larger calculation, but the declaration itself only certifies this single equality.

In the Recognition Science framework, such declarations are part of a machine-checked library of formal theorems. The library is a collection of statements that have been verified by a computer program, so there is no gap between what is stated and what is checked. The declaration e_210003 does not by itself prove anything about gravity, space, or the structure of the universe. It is a precise, narrow arithmetic fact that could serve as a step in a longer argument, but its content is exactly the equality it states and nothing more.

What the declaration does not claim is worth stating plainly. It does not claim that the equality holds for all positions, only for the one position named by the six coordinates. It does not claim that the numbers have any physical meaning, nor that the calculation is part of a complete theory of gravity. The declaration is silent on all of that. It is a single verified line in a long ledger of formal work, and its value is that it is exact, not that it is grand.

theorem e_213333 : m2Num 2 1 3 3 3 3 = 8 * explicitZ 2 1 3 3 3 3 := by decide

theorem e_213333 : m2Num 2 1 3 3 3 3 = 8 * explicitZ 2 1 3 3 3 3 := by decide

What this page does not claim

The declaration does not prove that the equality holds for all positions, only for the one named. The declaration does not assign any physical meaning to the numbers m2Num or explicitZ. The declaration does not by itself establish any claim about gravity or the structure of space.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk09.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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