Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk02 E 020003

A checked arithmetic identity

In the Recognition Science framework's machine-checked library of formal theorems, the declaration e_020003 is one small, specific result. It states that for a particular set of six indices, the value of a function called m2Num equals 8 times the value of another function called explicitZ. The proof is a direct computation: the kernel checks the arithmetic by deciding the equality, with no additional axioms beyond the standard three.

This identity lives inside a much larger project: the ReggeExactMidpointM2TTIdentity4D module, which appears to be part of a gravity analysis. The name suggests it concerns a discrete approximation to gravity, likely involving a Regge calculus approach where spacetime is built from flat simplices. The specific chunk, M2NumChunk02, contains dozens of similar theorems, each for a different set of indices, all proving the same form of identity: m2Num = 8 * explicitZ.

The declaration e_020003 itself does not claim anything about gravity, physics, or the framework's broader results. It is purely an arithmetic statement about two functions defined within the library. The theorem establishes a numerical relationship for one specific input, verified by the kernel's computation. It does not derive the Einstein field equations, does not prove the Regge calculus converges to general relativity, and does not establish any physical law.

What the declaration does is provide a verified building block. Within the framework, such identities are part of a larger structure that aims to derive physical laws from first principles. This particular theorem is a small, checked step in that process, confirming that the functions behave as expected for this one case. It illustrates the framework's approach of breaking down complex claims into machine-verifiable pieces, but it is not itself a claim about the physical world.

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 declaration does not prove anything about gravity or physics. This declaration does not derive the Einstein field equations. This declaration does not establish that Regge calculus converges to general relativity.

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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