Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk00 E 000010

A numerical identity

In numerical analysis, a calculation is only as trustworthy as its verification. The declaration e_000010 is one line in a long chain of such verifications. It states that for a particular set of six index values, the quantity m2Num equals 8 times the quantity explicitZ. The proof is by direct computation, a method the machine-checked library of formal theorems accepts as conclusive for this finite case.

The context is a study of gravity using Regge calculus, a discrete approach where spacetime is approximated by flat pieces. The declaration sits in a file whose docstring says it is chunk 0 of a larger computation, and that this chunk involves 256 kernel decisions. Each decision is a small, checkable step. The declaration e_000010 is one such step, confirming an identity for the indices 0, 0, 3, 1, 3, 3. The pattern of neighboring declarations shows the same identity holds for many nearby index combinations, suggesting a systematic structure rather than a one-off coincidence.

What this declaration does not do is prove the overall gravity result. It verifies a single numerical equality, not the physical theory behind it. The identity is a building block, not the building. The declaration also does not claim that the identity holds for all indices; it is specific to the listed values. The machine-checked proof is exact for this case, but the broader claim, that these two quantities are related by a factor of 8 across all relevant indices, would require a separate, more general theorem.

theorem e_003133 : m2Num 0 0 3 1 3 3 = 8 * explicitZ 0 0 3 1 3 3 := by decide

theorem e_003133 : m2Num 0 0 3 1 3 3 = 8 * explicitZ 0 0 3 1 3 3 := by decide

What this page does not claim

The declaration does not prove the overall gravity result, only a single numerical equality. The identity is not claimed to hold for all indices, only for the specific values listed in the declaration. The declaration does not establish the physical theory behind the Regge calculus approach.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk00.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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