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No Szöllősi matrix lies in a quadruplet of mutually unbiased bases in dimension six

Anonymous

Published Sep 30, 2026• 0 citations
Publisher

Abstract

Unrefereed candidate excluding the specified closed two-circulant Szollosi family from MUB quadruplets in complex dimension six. The Fourier-family result re-proves prior work. The unrestricted dimension-six maximum remains conditional on MMVW Conjecture 2. The package separates an untrusted hull generator from an interval and graph checker; canonical half-open ownership repairs boundary coverage, and input-bound clean replay prevents stale cache acceptance. No end-to-end formal verification, unaffiliated reproduction or external human peer review is claimed. See the replay receipt for exact measured scope. Original prose and data CC0; original code MIT; third-party and review material retain their terms.

DOI
10.5281/zenodo.23051061

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Title. An Independent Reproduction and Four Extensions of the MUB(6) Fourth-Vector Feasibility Wall Abstract. We present a companion note that cites N. Erlwein’s exact fourth-vector feasibility wall for a canonical mutually unbiased product triple in dimension six (Zenodo 20682233; theorem W = (88 + 3√6)/100). We do not redistribute the upstream software bundle. Independently, we (A) maintain a pure-Rust exact verification surface; (B) raise a d=10 closed-form hunt to a 460-decimal-place stationarity anchor with a widened PSLQ menu (no relation found); (C) run a full Cl(2)×Cl(5) single-qudit Clifford census at d=10, finding a single antiunitary Z/2 real structure; and (D) issue exact rational finite-cover exclusion certificates on a specified cell of the gauge-fixed candidate 5-torus. MUB(6)=3 and MUB(10) remain open. Local certificates mint no authority. Why a researcher should care. The note strengthens a rare exact, machine-checkable obstruction artifact in d=6 quantum information with a second language (Rust), higher-precision d=10 evidence, and independently checkable finite covers—while keeping claim boundaries explicit. What this does not claim. Not MUB(6)=3; not MUB(10); not a closed form at d=10; not joint authorship of Erlwein’s wall; not a global moduli theorem. Reproduction. cd crate && cargo test -j 1cargo run --release --bin mub_cover -- --region quadrant DOI. Pending human mint. Upstream wall: 10.5281/zenodo.20682233.

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Unrefereed candidate excluding the specified closed two-circulant Szollosi family from MUB quadruplets in complex dimension six. The Fourier-family result re-proves prior work. The unrestricted dimension-six maximum remains conditional on MMVW Conjecture 2. The package separates an untrusted hull generator from an interval and graph checker; canonical half-open ownership repairs boundary coverage, and input-bound clean replay prevents stale cache acceptance. No end-to-end formal verification, unaffiliated reproduction or external human peer review is claimed. See the replay receipt for exact measured scope. Original prose and data CC0; original code MIT; third-party and review material retain their terms.
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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.
Unrefereed mathematical candidate. Exact counterexamples to a proposed universal mixed-state total concentratable-entanglement upper bound, including full-rank noisy and genuinely tripartite-entangled families; sharp uniform and fixed-size concave-roof impurity repairs. Analytic proofs and producer-side exact arithmetic checks are provided. AI-assisted internal review does not establish external peer review, independent reproduction, formal verification, priority or impact. Original prose and data CC0-1.0; original code MIT. Source literature retains its own terms.
Title. An Independent Reproduction and Four Extensions of the MUB(6) Fourth-Vector Feasibility Wall Abstract. We present a companion note that cites N. Erlwein’s exact fourth-vector feasibility wall for a canonical mutually unbiased product triple in dimension six (Zenodo 20682233; theorem W = (88 + 3√6)/100). We do not redistribute the upstream software bundle. Independently, we (A) maintain a pure-Rust exact verification surface; (B) raise a d=10 closed-form hunt to a 460-decimal-place stationarity anchor with a widened PSLQ menu (no relation found); (C) run a full Cl(2)×Cl(5) single-qudit Clifford census at d=10, finding a single antiunitary Z/2 real structure; and (D) issue exact rational finite-cover exclusion certificates on a specified cell of the gauge-fixed candidate 5-torus. MUB(6)=3 and MUB(10) remain open. Local certificates mint no authority. Why a researcher should care. The note strengthens a rare exact, machine-checkable obstruction artifact in d=6 quantum information with a second language (Rust), higher-precision d=10 evidence, and independently checkable finite covers—while keeping claim boundaries explicit. What this does not claim. Not MUB(6)=3; not MUB(10); not a closed form at d=10; not joint authorship of Erlwein’s wall; not a global moduli theorem. Reproduction. cd crate && cargo test -j 1cargo run --release --bin mub_cover -- --region quadrant DOI. Pending human mint. Upstream wall: 10.5281/zenodo.20682233.