Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk04 E 100013

A single checked identity

The declaration theorem e_100013 is a single, machine-checked arithmetic statement inside a larger formal project. It asserts that a particular numerical expression, called m2Num with six index values, equals eight times another expression called explicitZ with the same six indices. The proof is a direct computation: the line "by decide" means the computer evaluates both sides and confirms they are equal. This is not a new physical law; it is a verified row in a ledger of thousands of similar identities.

The context places this identity within a study of Regge calculus, a discrete approximation to general relativity where spacetime is built from flat simplices. The project aims to show that a certain midpoint evaluation of a second-order quantity satisfies an identity related to the trace of the Einstein tensor. Each e_xxxxxx theorem, including e_100013, checks one numerical case of that identity. The name "chunk 4" indicates this file covers a block of 256 such cases, and the docstring notes that the kernel decides each one.

In Recognition Science, this identity is part of a bridge between its foundational cost formalism and conventional gravitational physics. The framework models reality as a discrete record of recognition events, and it derives constants and structures from that starting point. Here, the framework's library of formal theorems verifies that its numerical machinery reproduces a known gravitational identity in a specific discretized setting. The value of e_100013 is that it contributes one more confirmed case to that bridge, strengthening the evidence that the framework's internal mathematics aligns with standard Regge calculus.

What e_100013 does not claim is broader than what it does. It does not prove the identity for all indices; it checks exactly one combination. It does not establish the physical validity of Regge calculus or of the Recognition Science framework itself. It says nothing about whether the discretization converges to the continuum limit of general relativity. The declaration is a piece of arithmetic confidence, not a statement about the nature of spacetime. Its role is to make the larger project auditable: every numerical case is independently verified by the kernel, so the bridge rests on checked computation rather than on unexamined symbolic manipulation.

theorem e_103333 : m2Num 1 0 3 3 3 3 = 8 * explicitZ 1 0 3 3 3 3 := by decide

theorem e_103333 : m2Num 1 0 3 3 3 3 = 8 * explicitZ 1 0 3 3 3 3 := by decide

theorem e_103333 : m2Num 1 0 3 3 3 3 = 8 * explicitZ 1 0 3 3 3 3 := by decide

What this page does not claim

The declaration does not prove the identity for all index values, only for the single six-tuple it names. The declaration does not establish that Regge calculus converges to continuum general relativity. The declaration does not validate the physical assumptions of the Recognition Science framework.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk04.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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