Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk01 E 010003

A verified arithmetic identity

The declaration e_010003 is a machine-checked proof that a particular arithmetic identity holds. The identity states that a quantity called m2Num, evaluated at a specific set of six indices, equals eight times another quantity called explicitZ at the same indices. The indices are written as a tuple like 0 1 3 3 3 3, and the proof covers a block of these tuples. The verification method is direct computation: the proof checker evaluates both sides and confirms they are equal.

This is a routine but necessary step within a larger project. The project, called Recognition Science, builds physical and mathematical structure from a single starting point: reality keeps a ledger, a discrete record of recognition events, and the cost of recognition is forced, not chosen. The work here concerns gravity analysis, specifically a calculation labeled ReggeExactMidpointM2TTIdentity4D. The identity e_010003 is part of a chunk of many similar identities, each verifying the same pattern for different index values.

The declaration is a theorem in the framework's machine-checked library of formal theorems. Its proof uses the `decide` tactic, meaning the computer checks the arithmetic directly. This makes the claim about this specific numerical equality airtight within the formal system. The broader significance is that it contributes to a verified chain of reasoning about a gravity-related identity, though the physical interpretation of the quantities m2Num and explicitZ is not established by this declaration alone.

What e_010003 does not claim is as important as what it proves. It does not assert any physical law, nor does it define what m2Num or explicitZ mean. It does not claim that the identity holds for all indices, only for the specific ones listed. It does not connect this arithmetic fact to the measured value of any physical constant. The declaration is a precise, narrow, and fully verified computational step, not a statement about the nature of gravity itself.

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

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

This declaration does not establish any physical law or interpretation of the quantities involved. This declaration does not prove the identity holds for all possible index values. This declaration does not connect the arithmetic result to any measured physical constant.

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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: