Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk02

A checked arithmetic block

This block is a piece of a larger, machine-checked library of formal theorems. Its name describes its role: it is part of a gravity analysis, specifically checking an identity related to the Regge calculus, a discrete approach to general relativity where spacetime is built from flat pieces. The identity in question, called the midpoint M2 TT identity, relates two different ways of computing a quantity, and this block checks that the relationship holds for a particular range of inputs.

The core statement is simple. The block defines a function m2Num and a function explicitZ, and it proves that for a range of six-index inputs, the first is exactly eight times the second. For example, one theorem states that m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3. The proof for each case is by decide, meaning the computer directly computes both sides and confirms they are equal. This is not a symbolic proof; it is a direct numerical verification for each specific set of indices.

The block covers a range of index combinations, starting with 0 2 3 3 3 3 and working down through systematic variations. The documentation notes this is chunk 2 of a larger computation, with 256 kernel decisions in this part. Each theorem is a small, self-contained fact, and together they form a verified table of values. The significance is that these checks are part of a broader effort to confirm that a complex identity from a discrete theory of gravity holds exactly, not approximately, for a wide range of cases.

In plain language, this block is a piece of bookkeeping. It takes a formula from a discrete model of gravity and verifies, number by number, that a certain relationship is true. The value of this is not in any single equation, but in the cumulative assurance that the identity is not a fluke of one particular case. It is a small brick in a wall of formal verification, where every claim is checked by a computer rather than assumed.

theorem e_023333 : m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3 := by decide

theorem e_023333 : m2Num 0 2 3 3 3 3 = 8 * explicitZ 0 2 3 3 3 3 := by decide

What this page does not claim

This block does not prove the midpoint M2 TT identity for all possible inputs, only for the specific block of indices listed. This block does not provide a physical interpretation of the identity it verifies. This block does not derive the Regge calculus or the identity from first principles.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk02.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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