Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk15 E 330011

A single verified arithmetic identity

The declaration e_330011 is a single, fully verified arithmetic statement inside a machine-checked library of formal theorems. It states that a particular function, called m2Num, when given the six numbers 3, 3, 0, 0, 1, 1, produces a value exactly eight times the value of another function, explicitZ, given the same six numbers. In symbols: m2Num 3 3 0 0 1 1 = 8 * explicitZ 3 3 0 0 1 1. The proof is computational: the library's checker directly evaluates both sides and confirms they are equal.

This identity is one of 256 similar statements in a file that systematically checks all possible six-number combinations drawn from the digits 0, 1, 2, and 3. The file's docstring names this as chunk 15 of a larger verification effort. Each theorem in the chunk, including e_330011, follows the same pattern: for a specific six-number input, the m2Num function equals eight times the explicitZ function. The proof method, called decide, means the computer program simply calculates both sides and confirms the equality holds. The declaration does not explain what m2Num or explicitZ represent physically, nor does it derive any general law from this single case.

In Recognition Science, this kind of statement is a building block. The framework's library uses many such verified identities to support larger proofs about gravity and geometry. The declaration e_330011 is a proven theorem in the sense that its arithmetic is checked by the machine, but it is not a claim about the physical meaning of the functions involved. It does not assert that the number 8 has any physical significance, nor that the pattern holds for all possible inputs. It simply records one exact numerical relationship that the library has verified.

What this declaration does not claim is as important as what it proves. It does not claim that m2Num and explicitZ are equal in general, only for this specific input. It does not claim that the factor of 8 appears in any other context or has a physical interpretation. It does not claim that the functions themselves are defined in any particular way; their definitions are separate statements in the library. The theorem is a precise, narrow fact: for the six numbers 3, 3, 0, 0, 1, 1, one function's output is exactly eight times the other's.

theorem e_333333 : m2Num 3 3 3 3 3 3 = 8 * explicitZ 3 3 3 3 3 3 := by decide

theorem e_333333 : m2Num 3 3 3 3 3 3 = 8 * explicitZ 3 3 3 3 3 3 := by decide

theorem e_333333 : m2Num 3 3 3 3 3 3 = 8 * explicitZ 3 3 3 3 3 3 := by decide

What this page does not claim

The declaration does not claim that m2Num equals eight times explicitZ for any input other than 3, 3, 0, 0, 1, 1. The declaration does not claim any physical meaning for the number 8 or for the functions themselves. The declaration does not claim that the pattern holds for all possible six-number combinations.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk15.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: