Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk11 E 230013

A checked arithmetic identity

The declaration e_230013 is one entry in a large machine-checked library of formal theorems. The library proves statements by reducing them to simple computation. This particular entry checks a small piece of arithmetic inside a larger gravity analysis. It states that a function called m2Num, when given the six numbers 2 3 0 0 1 3, produces a value exactly equal to 8 times another function called explicitZ given the same six numbers. The proof is the word decide, which means the computer evaluates both sides and confirms they are identical.

The context names the file ReggeExactMidpointM2TTIdentity4D. The name suggests the calculation sits in a study of exact midpoint rules for a four-dimensional theory related to Regge calculus, a discrete approach to general relativity. The functions m2Num and explicitZ are not defined in this file. The declaration only establishes the equality for this one specific input tuple. It does not prove the equality holds for all inputs, nor does it explain what the numbers 2, 3, 0, 0, 1, 3 mean physically. The theorem is a local check, a single verified line in a larger proof effort.

What the declaration does not claim matters as much as what it proves. It does not claim that the gravity theory is correct, that the midpoint rule is physically accurate, or that the numbers 2, 3, 0, 0, 1, 3 correspond to any particular physical quantity. It does not establish any law of gravity or any property of spacetime. It merely confirms that for this one tuple, the computed value m2Num matches the explicit formula 8 times explicitZ. The broader significance, if any, lives in the surrounding theory and other theorems, not in this isolated line.

In plain terms, e_230013 is a receipt. It says: for this one input, the two ways of computing the same quantity agree. The machine checked it, and the check passed. A reader should take from this page exactly that fact, and not more. The value of such declarations is cumulative: thousands of small verified steps can build a large trustworthy proof, but each step alone carries only its own narrow content.

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 prove any physical law of gravity. The declaration does not establish that the midpoint rule is physically accurate. The declaration does not define the functions m2Num or explicitZ.

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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