Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk00 E 000013

A single verified identity

In numerical analysis, a large computation is often checked by verifying a single, specific instance of a general formula. The declaration e_000013 is exactly such a check. It states that for a particular set of six indices, the value of a function called m2Num equals eight times the value of another function called explicitZ. The proof is not a symbolic derivation; it is a direct computation, finished by the kernel's decide tactic, which means the equality was verified by evaluating both sides completely.

This identity is part of a larger family of similar statements, all sharing the same form: m2Num 0 0 i j k l = 8 * explicitZ 0 0 i j k l. The indices i, j, k, l each range over the values 0, 1, 2, 3. The declaration e_000013 covers one specific combination of these indices, and the machine-checked library contains hundreds of such theorems, each one a separate, independently verified instance.

The purpose of this collection is to provide a rigorous, point-by-point confirmation of a numerical relationship that appears in the framework's analysis of gravity. By proving each case with a computation that leaves no room for error, the library establishes that the relationship between m2Num and explicitZ holds exactly for these inputs. This is a concrete, verified fact, not a statistical check or an approximate match.

What this declaration does not do is prove the relationship for all possible indices. It does not establish a general theorem that m2Num is always eight times explicitZ. Each of the hundreds of declarations is a separate, finite check for its own specific indices. The declaration also says nothing about what m2Num or explicitZ mean physically; it only certifies the numerical equality between the two computed values for this one case.

theorem e_003333 : m2Num 0 0 3 3 3 3 = 8 * explicitZ 0 0 3 3 3 3 := by decide

theorem e_003333 : m2Num 0 0 3 3 3 3 = 8 * explicitZ 0 0 3 3 3 3 := by decide

What this page does not claim

This declaration does not prove the relationship m2Num = 8 * explicitZ for all possible index combinations. This declaration does not provide any physical interpretation for the functions m2Num or explicitZ. This declaration does not establish any general theorem about gravity; it only verifies a single numerical instance.

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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