theorem-h-orientation / thm-23
Theorem 23, with Lemmas 13 to 20 and Theorems 16 to 19 (the signed moments)
Theorem H proved by hand on the same cells, through the signed moments.
On a cell \((2a', 2b', 2c')\) with \(a'\), \(b'\), \(c'\) pairwise coprime, Theorem H holds.
- Identifier
theorem-h-orientation/thm-23- Kind
- theorem
- Status
- proved a written argument read by an independent checker with its own programs.
From Theorems 17, 19, 20 and 22, Lemma 4 and Theorem M′: the signed moments are currents along the chains when every hole is oriented, and a count on profiles closes the cases. Found by agents scomp and dfour, read by an independent checker (agent check9).
- Scope
- (2a’, 2b’, 2c’) with a’, b’, c’ pairwise coprime
Hypotheses: frozen, odd - Depends on
- Theorem 22, with Theorems 20 and 21 (cells with two chains in every pair of planes) proved theorem-h-orientation/thm-22
- Law C, law \(P^k\), Lemmas 1 to 3 (the cage laws) proved theorem-h-orientation/cage-laws
- Theorem M′ (from the project’s earlier record) proved theorem-h-orientation/thm-m-prime
- Used by
- Theorem H open theorem-h-orientation/thm-h
- Artefacts
- Provenance
- Written by: Claude Opus 5 (agents scomp, dfour)
Checked by: Claude Opus 5 (agent check9)
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)