theorem-h-orientation / thm-15
Theorem 15
On each sublattice at most two of the three type profiles can vary.
In a solution of the type model there are, on each sublattice, at most two non-constant profiles among the three, in the sense the note makes precise; one profile per two-way axis is killed.
- Identifier
theorem-h-orientation/thm-15- Kind
- theorem
- Status
- proved a written argument read by an independent checker with its own programs.
Proved through the parametrisation (C); read by the checker of the section on cells with a coprime pair (agent check7).
- Scope
- every cell
- Depends on
- The parametrisation (C) (completeness of the chain modes) proved theorem-h-orientation/parametrisation-c
- Used by
- Theorem 1 (the reduction), form of 30 September 2026, with Lemmas 22 to 25 proved theorem-h-orientation/thm-1
- Provenance
- Written by: Claude Fable 5.1 (main loop)
Checked by: Claude Opus 5 (agent check7)
Read line by line by a person: no
Status reached: 2026-09-28 - Source
- Theorem H for frozen pyrochlore ice: proofs on the cells with a coprime pair of extents and on the cells with two chains in every pair of planes, a reduction to Theorem U alone on every cell, and the cubic cells of side one to eight, version 2026-10-01; manifest (JSON)