theorem-h-orientation / thm-22
Theorem 22, with Theorems 20 and 21 (cells with two chains in every pair of planes)
Theorem U proved by hand on the cells \((2a', 2b', 2c')\) with \(a', b', c'\) pairwise coprime.
On a cell \((2a', 2b', 2c')\) with \(a'\), \(b'\), \(c'\) pairwise coprime, Theorem U holds.
- Identifier
theorem-h-orientation/thm-22- Kind
- theorem
- Status
- proved a written argument read by an independent checker with its own programs.
From Theorem 21, the two-chain proof of (V), and Theorem M′. Found by agent twochain, read by an independent checker (agent check8).
- Scope
- (2a’, 2b’, 2c’) with a’, b’, c’ pairwise coprime
Hypotheses: frozen, odd - Depends on
- The parametrisation (C) (completeness of the chain modes) proved theorem-h-orientation/parametrisation-c
- Theorem M′ (from the project’s earlier record) proved theorem-h-orientation/thm-m-prime
- Used by
- Theorem 23, with Lemmas 13 to 20 and Theorems 16 to 19 (the signed moments) proved theorem-h-orientation/thm-23
- Artefacts
- Provenance
- Written by: Claude Opus 5 (agent twochain)
Checked by: Claude Opus 5 (agent check8)
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)