Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk00 E 000003

A single algebraic check

The declaration e_000003 is one small theorem in a machine-checked library of formal mathematics. It states that for a particular six-index combination, the value of a function called m2Num equals eight times the value of a function called explicitZ. The indices in question are 0 0 3 3 3 3, and the equality is verified by the kernel's decide tactic, which computes both sides and confirms they match. This is a concrete, checkable fact, not a general statement about all indices.

The theorem belongs to a larger project within the Recognition Science framework, which models physical structure from a discrete record of events. Here, the framework is analyzing a four-dimensional gravitational identity, likely related to Regge calculus, a discrete approach to general relativity. The m2Num function appears to compute a numerical quantity from six indices, while explicitZ provides a reference value. The theorem e_000003 confirms that for this specific index tuple, the computed value is exactly eight times the reference.

This declaration is one of many similar theorems in the file, each covering a different six-index combination. Together, they build a checkable table of values, but each theorem stands alone. The proof is by computation, meaning the kernel directly evaluates both sides and finds them equal. This is a verification of a specific instance, not a derivation of a general law or a proof of the underlying identity for all cases.

What e_000003 does not claim is broader significance. It does not prove that the identity holds for all indices, nor does it explain why the factor of eight appears. It does not connect this numerical check to any physical prediction or to the forcing chain that derives constants like the golden ratio. It is a single, verified algebraic fact, a small brick in a much larger wall. The reader can trust that this one equality is correct, but the meaning of the equality, and its role in the wider theory, is established elsewhere, if at all.

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 theorem does not prove the identity for all six-index combinations. This theorem does not establish any physical law or prediction. This theorem does not derive the factor of eight 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/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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