Gravity Analysis Regge Bloch Orbit Transport4 D Orbit Covering Perm T11 Eq Slot

Covering permutations

In the Recognition Science framework's study of 4D Regge Bloch transport, a lattice is divided into 240 slots, each identified by a pair of coordinates. A recognition ledger, a discrete record of how events relate, assigns each slot an orbit type and a covering permutation, a reordering of 24 coordinate axes that lets data move from one slot to another. The declaration orbitCoveringPerm_t11_eq_slotTransportPerm proves a specific agreement: for every slot of the simplest orbit type, called t11, the general covering rule gives exactly the same permutation as a hand-written table named slotTransportPerm.

The theorem is checked by exhaustive computation over all 240 slots, with no gaps and no unproved assumptions. It confirms that the general covering rule, which works for every orbit type, does not disagree with the older table on the one case the table was built for. The table itself is marked as valid only for t11 slots; the theorem does not extend that table to other orbit types. The general rule remains the authority for all slots, and the theorem is a consistency check, not a new transport law.

What the declaration does not claim is just as precise. It does not say that the hand table works for any other orbit type, and it does not say the covering rule is unique or optimal. It only establishes that on t11 slots, two different ways of producing a permutation agree. The proof is a finite case check, so it carries no information about why the agreement holds, only that it does. In plain terms: the machine has verified that the general method and the old table tell the same story on the simplest ground, and the page leaves the broader story to other theorems.

/-- On `(1,1)` slots the covering perm agrees with the legacy table. -/
theorem orbitCoveringPerm_t11_eq_slotTransportPerm (s : Fin 24) (t : Fin 10) :
    orbitCoveringPerm .t11 s t = slotTransportPerm s t := by
  fin_cases s <;> fin_cases t <;> decide

What this page does not claim

The hand table is valid for any orbit type other than t11. The covering rule is unique or optimal among all possible permutations. The theorem explains why the agreement holds, only that it holds.

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/ReggeBlochOrbitTransport4D.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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