Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk10 E 220002

A verified arithmetic identity

The declaration e_220002 establishes a precise arithmetic equality. 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 at those same indices. The proof is carried out by the decide tactic, meaning the equality is verified by direct computation, not by a longer chain of reasoning.

This equality is one instance in a larger pattern. The surrounding declarations, such as e_223333 and e_223332, show the same relationship holding for many other index combinations. Together they suggest that for this entire family of index tuples, the function m2Num is consistently eight times explicitZ. The declaration e_220002 specifically confirms this for the index tuple (2, 2, 0, 0, 0, 2).

In plain terms, this is a bookkeeping check. The framework is verifying that a complicated numerical quantity, m2Num, which may arise from a physical calculation, matches a simpler reference quantity explicitZ scaled by a factor of eight. This is a common and necessary step in building confidence that a large formal development is internally consistent.

In Recognition Science, this declaration is part of a broader effort to connect its abstract principles to concrete calculations. The framework models physical structure through a discrete record of events, and this kind of exact numerical verification is how it grounds abstract theorems in specific instances. The declaration does not, however, make any statement about the physical meaning of the numbers themselves, nor does it claim that the factor of eight has any physical significance beyond being a mathematical result of the computation.

theorem e_223333 : m2Num 2 2 3 3 3 3 = 8 * explicitZ 2 2 3 3 3 3 := by decide

What this page does not claim

The declaration does not assign physical meaning to the numbers m2Num or explicitZ. The declaration does not prove that the factor of eight holds for all possible index tuples. The declaration does not by itself establish any result about gravity or spacetime.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk10.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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