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O-01d0 polar-fibre structural reductions: Exact identities, failed proof architectures, and executable remaining gates

Anonymous

Published Aug 28, 2026• 0 citations
Publisher

Abstract

Anonymous unrefereed structural-reductions candidate with written proofs, fixed-index producer evidence, exact bounded falsifications, bounded computations, and executable remaining gates. O-01d0 and all linked headline conjectures remain open. Original prose/data are CC0-1.0 and original code is MIT; see LICENSES.md.
DOI
10.5281/zenodo.22143954

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Unrefereed mathematical candidate: a faithful-Pauli converse to the even-hole, claw-free global spectrum theorem; an exact central-sector criterion; explicit all-coupling periodic Fendley blocks at N=8,9; weak prescribed-mode heredity; and a repaired three-mode parity-completeness argument. Written proofs, exact computer-algebra certificates for 107 listed graphs, and numerical census evidence have separate assurance boundaries. Producer replay and a separately implemented model-review checker are not external human peer review, unaffiliated reproduction, formal verification or exhaustive novelty. The remaining 1621 numerical candidates are not all-coupling certified. Original prose/data CC0-1.0; original code MIT; third-party exclusions in LICENSES.md.
For homogeneous open nearest-neighbour chains with a normalised rank-one local projector whose forbidden vector has exactly two equal nonzero Schmidt probabilities, a written proof candidate classifies gappedness in every finite local dimension. Gaplessness is equivalent to a balanced-marker form and has exact finite-length gap 1−cos(π/N). All other interactions in the class have explicit uniform lower bounds. A complete qutrit short-spectrum fibre has fixed Schmidt probabilities, two- and three-site spectra and ground-space dimension at every length, yet only its endpoint is gapless. The proof distinguishes compatible propagation from an obstruction to four-site saturation. Unrefereed candidate. Producer-side exact and numerical replay corroborates finite statements, not universal analytic proofs. Supplied referee implementation and review are not authenticated unaffiliated reproduction or peer review. No exhaustive priority, experimental or impact claim. Version 1.0.1 repairs the symbolic classifier domain and adds precise antecedent locators and a named full Gram-decomposition lemma with explicit basis appendix. Original prose/data CC0-1.0; original code MIT; third-party exceptions in LICENSES.md.