Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk05 E 110003

A numerical identity in a gravity computation

Large physics calculations are often built from thousands of smaller steps. Each step must be exactly right, or the final result inherits the error. The declaration e_110003 is one such step: it is a theorem in the framework's machine-checked library of formal theorems that verifies a specific numerical identity used inside a gravity analysis.

The identity concerns two functions, m2Num and explicitZ, which appear in a computation related to Regge calculus, a discrete approach to general relativity. For a particular set of six indices, the theorem states that m2Num applied to those indices equals 8 times explicitZ applied to the same indices. The proof is by direct computation, using the ledger, a discrete record of events, to decide the equality. The theorem is one of many in a chunk of the library that verifies this identity across a range of index values.

In plain terms, the declaration establishes that for this specific input, the two functions agree up to the constant factor 8. It is a local check, not a general law. It does not define what m2Num or explicitZ mean, nor does it prove that the identity holds for all inputs. It only confirms this one instance, and its neighbors confirm the same pattern for nearby index combinations.

The value of such a theorem is in the guarantee it provides. Because the proof is machine-checked, there is no room for a subtle arithmetic slip. The calculation is exact, not approximate. This matters in a framework where the cost of recognition is forced, because the framework's larger results depend on such precise intermediate steps.

theorem e_113333 : m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3 := by decide

theorem e_113333 : m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3 := by decide

What this page does not claim

This declaration does not prove the identity for all index values. It does not define the functions m2Num or explicitZ. It does not establish any physical law about gravity on its own.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk05.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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