Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk08 E 200001

A verified numerical identity

The declaration e_200001 is a theorem in the Recognition Science framework's machine-checked library of formal theorems. It states a precise numerical identity: for the index tuple 2 0 0 0 0 1, the computed value m2Num 2 0 0 0 0 1 equals 8 times the explicitly defined reference value explicitZ 2 0 0 0 0 1. In plain terms, the framework proves that a particular quantity in its gravity analysis, indexed by six coordinates, is exactly eight times a separately defined baseline quantity for that same index.

This theorem is part of a larger file, ReggeExactMidpointM2TTIdentity4DM2NumChunk08.lean, which contains a series of similar identities for many six-index tuples. The docstring describes the file as covering "m2Num = 8·explicitZ, chunk 8 (256 kernel decides)". This means the file verifies, for a block of 256 index combinations, that the m2Num function equals eight times the explicitZ function. The proof method is "by decide", which means the Lean kernel directly computes and checks the equality, providing a fully verified result without any unproven assumptions.

In the Recognition Science framework, such numerical identities are not isolated facts. They are part of a chain of theorems that force physical structure from a single starting point: a cost function for recognition events. The framework's central result proves that any cost function satisfying five plain conditions must equal a specific form, and from that form, a chain of theorems forces the golden ratio, an eight-tick cycle, 2^3, and three spatial dimensions. This particular identity, relating m2Num to explicitZ, is a small piece of that larger forcing chain, specifically within the gravity analysis portion.

The theorem does not claim that m2Num or explicitZ represent physical quantities in conventional physics. It does not assert that the number 8 has any physical significance beyond this algebraic relationship. It does not claim that the identity holds for all indices, only for the specific tuples verified in this file. The theorem is a formal statement about the relationship between two defined functions within the framework's own mathematical structure.

What this declaration establishes is a verified computational fact: within the Recognition Science framework, for the index 2 0 0 0 0 1, the value of m2Num is exactly eight times the value of explicitZ. This is a theorem proved in the machine-checked library, meaning it is axiom-clean and verified by the kernel. It is one of many such identities that together form a computational foundation for the framework's gravity analysis, but it is not a claim about the physical world beyond the framework's own definitions.

theorem e_203333 : m2Num 2 0 3 3 3 3 = 8 * explicitZ 2 0 3 3 3 3 := by decide

theorem e_203333 : m2Num 2 0 3 3 3 3 = 8 * explicitZ 2 0 3 3 3 3 := by decide

theorem e_203333 : m2Num 2 0 3 3 3 3 = 8 * explicitZ 2 0 3 3 3 3 := by decide

What this page does not claim

This theorem does not claim that m2Num or explicitZ represent physical quantities in conventional physics. This theorem does not assert that the identity holds for all possible index tuples, only for those verified in this chunk. This theorem does not claim that the number 8 has any physical significance beyond this algebraic relationship.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk08.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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