Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk03 E 030010

A kernel-checked arithmetic fact

The declaration e_030010 is a machine-checked theorem in the Recognition Science framework's library of formal theorems. It states that for a specific set of six numerical inputs, the value of a function called m2Num equals exactly eight times the value of another function called explicitZ. The proof is not a lengthy argument; it is a direct computational check, written in the Lean language and verified by the kernel, the core of the proof assistant that checks every step.

This identity is part of a larger calculation in the framework's gravity analysis, specifically in a file named ReggeExactMidpointM2TTIdentity4D. The broader context, as described in the file's docstring, is that a quantity called m2Num is being compared to eight times a quantity called explicitZ. The declaration e_030010 is one of many similar theorems in the file, each covering a different combination of the six inputs. The docstring notes that this particular chunk of 256 such checks is decided by the kernel, meaning each one is a direct computation that the proof assistant can confirm automatically.

What this declaration establishes, in plain terms, is a precise arithmetic fact: for the specific inputs it names, the two functions agree up to the factor of eight. It does not, by itself, explain what m2Num or explicitZ physically represent, nor does it prove any general law of gravity. It is a single verified step in a much longer chain of reasoning, a check that the numbers line up as the framework's larger theory expects them to.

theorem e_033333 : m2Num 0 3 3 3 3 3 = 8 * explicitZ 0 3 3 3 3 3 := by decide

theorem e_033333 : m2Num 0 3 3 3 3 3 = 8 * explicitZ 0 3 3 3 3 3 := by decide

What this page does not claim

This declaration does not prove any general law of gravity. This declaration does not explain what the functions m2Num or explicitZ represent physically. This declaration does not establish the correctness of the entire gravity analysis, only this one arithmetic step.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk03.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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