Relations Between Orbits Do Not Walk the Door: Pair Conditions, Ordering Conditions, and the Price of "All Requirements"
Works paper #235's Door two (item D-220-237-64, grade B) at packet #509's re-sharpened price, branch (a): a non-orbitwise excluding requirement whose content is a relation between orbits. Gate reproduces paper #235's printed exhibits exactly and packet #509's exhaustion (128 admitted-orbit sets, 16 excluding all three P2 discards, 0 exceptions). Two relational candidates are constructed and enumerated: the pair condition (no two admitted states with energies summing to zero unless both are zero; 12 bad orbit pairs) satisfies 22 of 128 sets, including 6 unbounded sets admitting discards, so it excludes nothing unconditionally; conditioned on a kept positive-energy orbit, all 98 mixed sets violate it, but the pair it forbids there is exactly paper #235 Sec.2's splitting 0 -> (+E) + (-E) -- the stability content in relational dress. The ordering condition (admitted ranges pairwise ordered, lowest bounded below) is satisfied by only 8 of 128 sets and fails on the spectrum P2 itself returns, because the kept orbits' ranges overlap. Three extra-spectral species are priced: Fock-space boundedness implies the one-particle bound; Reeh-Schlieder-type clustering presupposes the spectrum condition in its proof; pairwise detailed balance reduces to packet #509's Gibbs candidate. Branch (b), an exhaustion over ALL requirements, is priced as unstatable as a single theorem -- any statable version fixes a class -- and is rewritten as a schema over stated classes. Disposition: strengthened in pricing a third time, not closed; the count of three postulated inputs, zero derivations stands unchanged. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.
Authors
- William Alexander Aldred
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-03
- DOI
- https://doi.org/10.5281/zenodo.23936573
- Primary Topic
- Advanced Operator Algebra Research
- Type
- preprint