Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk07 E 130002

A single verified arithmetic step

The declaration e_130002 is a single verified arithmetic step inside a much larger formal calculation. The calculation concerns an object called m2Num, which takes six arguments and returns some numeric value, and another object explicitZ with the same six arguments. The declaration asserts that for one particular choice of those six arguments, the value of m2Num equals eight times the value of explicitZ.

The proof is not a long derivation. The declaration carries the proof term "by decide", which means the Lean kernel checked the equality by direct computation. The kernel decided the statement is true by evaluating both sides and confirming they match. This is a theorem in the machine-checked library of formal theorems, and it is tagged as a theorem because it is a proved statement with no axioms beyond the standard ones.

What this declaration does not claim is important. It does not claim that m2Num equals eight times explicitZ for all possible arguments. It claims only the one instance, the specific tuple of six numbers written in the declaration. It does not explain what m2Num or explicitZ mean physically, nor does it connect them to gravity, Regge calculus, or any other part of the framework. The names of the enclosing module suggest a context involving gravity analysis and a midpoint identity, but the declaration itself carries no such content.

The value of this declaration is as a building block. Large formal proofs are assembled from many small steps like this one. Each step must be checked individually before the whole structure can be trusted. This declaration is one such checked step, and its role is to make the larger calculation complete.

theorem e_133333 : m2Num 1 3 3 3 3 3 = 8 * explicitZ 1 3 3 3 3 3 := by decide

What this page does not claim

The declaration does not claim the equality holds for any other choice of arguments. The declaration does not claim any physical meaning for 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/ReggeExactMidpointM2TTIdentity4DM2NumChunk07.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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