Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk07 E 130012

A verified arithmetic identity

The declaration e_130012 is one entry in a large table of numeric identities. The table is part of a computer-checked library of formal theorems, a collection where every statement is verified by a machine. The specific theorem states that for a particular set of six input numbers, the value of a function called m2Num equals eight times the value of another function called explicitZ. The proof is a direct computation, noted in the source as decide, meaning the machine simply calculates both sides and confirms they are equal.

This identity is one of many similar statements in the same file. The source describes the whole set as "m2Num = 8·explicitZ, chunk 7 (256 kernel decides)". The phrase "256 kernel decides" refers to the number of individual computation steps the machine performs to check all the identities in this chunk. The declaration e_130012 is the first of these, and the file contains dozens of others with the same form, each for a different set of six input numbers. The pattern is that for every combination tested, the two functions are related by the factor eight.

The name of the file places this work in a broader context: it concerns a "Regge exact midpoint" calculation in four dimensions, related to gravity analysis. However, the declaration itself does not interpret what m2Num or explicitZ mean physically. It only establishes a numerical relationship between them for specific inputs. The theorem is a piece of arithmetic infrastructure, a verified step that could support later results, but it does not by itself make any claim about the nature of gravity, the structure of space, or any physical law.

What the declaration does not claim is equally clear. It does not assert that the factor eight has any special meaning, nor that the identity holds for all possible inputs. It is checked only for the specific six-number combinations listed in the file. The theorem does not derive any physical constant, does not prove any property of the functions beyond this equality, and does not connect to the broader framework's results about the golden ratio or spatial dimensions. It is a small, verified fact, useful as a building block but not a statement about the world.

theorem e_133333 : m2Num 1 3 3 3 3 3 = 8 * explicitZ 1 3 3 3 3 3 := by decide

theorem e_133333 : m2Num 1 3 3 3 3 3 = 8 * explicitZ 1 3 3 3 3 3 := by decide

theorem e_133333 : m2Num 1 3 3 3 3 3 = 8 * explicitZ 1 3 3 3 3 3 := by decide

What this page does not claim

The declaration does not establish any physical law or property of gravity. The declaration does not prove the identity for all possible inputs, only for the specific listed combinations. The declaration does not assign meaning to the factor eight or to the functions it relates.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk07.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: