Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk11 E 230011

A verified arithmetic fact

The declaration e_230011 is a single verified arithmetic fact inside a much larger calculation. It states that a particular function value, written m2Num 2 3 3 0 1 1, equals 8 times another function value, written explicitZ 2 3 3 0 1 1. The proof is by decide, meaning a computer program directly computed both sides and confirmed they are equal. This is not a new physical law; it is a bookkeeping step, like checking that a row of numbers in a ledger adds up correctly.

The context places this fact within a study of gravity, specifically a four-dimensional analysis using Regge calculus, a method that approximates curved spacetime with flat pieces. The names suggest the calculation involves a midpoint value for something called M2, and the identity is part of a larger pattern. The declaration is one of 256 such checks in its chunk, each verifying a similar equality for different input values. The entire collection is part of a machine-checked library of formal theorems, meaning every step is verified by a computer, not just asserted.

In Recognition Science, this kind of verification is part of a broader program. The framework derives physical structure from a single cost function, and its library contains many such formal checks. This particular declaration does not itself prove any grand claim about gravity or the universe. It is a small, concrete piece of arithmetic that supports a larger structure, much as a single brick supports a wall. Its value lies in being completely certain: the equality is checked by the computer's kernel, leaving no room for human error in this step.

What this declaration does not claim is important. It does not assert that the function m2Num represents any specific physical quantity, nor that the equality has a direct physical interpretation. It does not prove that Regge calculus is correct, or that the larger calculation is physically meaningful. It only establishes that, given the definitions of these functions, the two sides of this one equation are equal. The meaning of the functions and the physical relevance of the calculation are separate questions, not settled by this single theorem.

theorem e_233333 : m2Num 2 3 3 3 3 3 = 8 * explicitZ 2 3 3 3 3 3 := by decide

theorem e_233333 : m2Num 2 3 3 3 3 3 = 8 * explicitZ 2 3 3 3 3 3 := by decide

theorem e_233333 : m2Num 2 3 3 3 3 3 = 8 * explicitZ 2 3 3 3 3 3 := by decide

What this page does not claim

The declaration does not assign any physical meaning to the functions m2Num or explicitZ. The declaration does not prove that the Regge calculus approach correctly models gravity. The declaration does not establish any property of the larger calculation beyond this single arithmetic equality.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk11.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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