Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk12 E 300010

A numerical check in a gravity identity

The declaration e_300010 is one entry in a large collection of machine-checked theorems. Each theorem in this collection verifies a specific numerical relationship used in a broader calculation. The broader calculation concerns a proposed identity in a model of gravity, and the collection breaks that identity into many small, checkable pieces. This particular declaration checks one such piece, confirming that a certain computed value equals eight times another computed value for a specific set of six numerical inputs.

The theorem states that for the inputs 3, 0, 3, 3, 3, and 3, the value of a function called m2Num equals eight times the value of a function called explicitZ. The proof is by a direct computational check, which means the Lean kernel evaluates both sides and confirms they are equal. This is not a general proof about all possible inputs, but a verification of one specific case. The result is recorded as a theorem with no gaps in its proof, and it relies only on the standard axioms of the underlying type theory.

This kind of verification is part of a larger effort to build a machine-checked library of formal theorems. The library aims to provide exact, verified results for a chain of reasoning that starts from basic principles and leads to physical constants and structures. Within that effort, this declaration is a small but necessary component, confirming that a particular numerical relation holds. The factor of eight is a concrete, checkable fact that supports the consistency of the larger identity.

The declaration does not claim that the larger gravity identity is true, nor does it establish any physical law. It does not derive the factor of eight from first principles; it verifies that the two functions agree for this one set of inputs. It also does not claim anything about other sets of inputs, which would require separate theorems. The result is a single, isolated numerical check, not a general statement about the behavior of the functions involved.

theorem e_303333 : m2Num 3 0 3 3 3 3 = 8 * explicitZ 3 0 3 3 3 3 := by decide

What this page does not claim

The declaration does not prove the larger gravity identity. The declaration does not derive the factor of eight from general principles. The declaration does not apply to any inputs other than the specific six listed.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk12.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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