Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk01 E 010012

A kernel-decided arithmetic identity

The declaration e_010012 is a theorem in the Recognition Science framework's machine-checked library of formal theorems. 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 by decide, meaning the Lean kernel computes both sides and confirms they are equal; no external axioms are used.

This identity is one of many similar statements in the file ReggeExactMidpointM2TTIdentity4DM2NumChunk01.lean. The file's docstring describes it as "m2Num = 8·explicitZ, chunk 1 (256 kernel decides)". The declaration e_010012 corresponds to the specific index tuple (0,1,0,0,1,2), and the theorem asserts that m2Num 0 1 0 0 1 2 = 8 * explicitZ 0 1 0 0 1 2. The surrounding declarations cover other index tuples in the same chunk, each with the same structure.

In plain terms, the theorem verifies a numerical relationship between two functions that appear in a larger calculation. The functions themselves are not defined in this file; their definitions live elsewhere in the library. The declaration does not introduce new physics, does not define the functions, and does not interpret what the equality means physically. It only certifies that a specific arithmetic equality holds, checked directly by the kernel.

The value of this theorem is in what it enables: a verified step in a longer chain of reasoning. Because the proof is by computation, it is exact and carries no approximation. The declaration is a building block, not a standalone result about gravity or recognition. It says nothing about the meaning of m2Num or explicitZ, only that for these indices, one is eight times the other.

theorem e_013333 : m2Num 0 1 3 3 3 3 = 8 * explicitZ 0 1 3 3 3 3 := by decide

theorem e_013333 : m2Num 0 1 3 3 3 3 = 8 * explicitZ 0 1 3 3 3 3 := by decide

What this page does not claim

The declaration does not define the functions m2Num or explicitZ. The declaration does not interpret the physical meaning of the equality. The declaration does not prove the identity for any index tuple other than (0,1,0,0,1,2).

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk01.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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