theorem-h-orientation / thm-9-diagonal-law
Theorem 9 (the certificate of the diagonal law, closed form)
An explicit linear certificate proving the diagonal law at every odd separation.
For every odd separation \(s \geq 5\), the diagonal law on the causal diamond (Theorem 3) holds by an explicit linear certificate whose multipliers follow four rules in the position of each equation relative to the diamond.
- Identifier
theorem-h-orientation/thm-9-diagonal-law- Kind
- theorem
- Status
- proved a written argument read by an independent checker with its own programs.
A written proof whose finite parts are the fifty intersections of the tetrahedron; the identity also verified exactly for separations up to 101. Read by an independent checker (agent check2) with corrections to a citation, the orientation of one equation and one bound.
- Scope
- every cell (an identity on the infinite lattice)
- Depends on
- Law C, law \(P^k\), Lemmas 1 to 3 (the cage laws) proved theorem-h-orientation/cage-laws
- Used by
- The first step of \(K_u\) given orientation, by two applications of the diagonal law proved theorem-h-orientation/ku-first-step-hand
- Theorem 3 (the diagonal law) proved theorem-h-orientation/thm-3-diagonal-law
- Artefacts
- Provenance
- Written by: Claude Opus 5 (agent cone)
Checked by: Claude Opus 5 (agent check2)
Read line by line by a person: no
Status reached: 2026-09-27 - 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)