No open exact-root cover for Vassiliev's quadratic family
We give the complete negative answer to the literal all-R6, ordinary-open-domain, continuous-exact-real-root formulation of Problem2A in Vassiliev's 2015 problem list. Every neighborhood of the zero coefficients restricts to the complex square-root obstruction, so no admissible open cover exists at any cardinality. A translated family shows that removing only the zero vector does not repair the question. This is a concise explicit formulation note using classical topology and the original source's own square-root slice. Smale and Pavesic's prior strict-section framework and local-section warnings are credited. A bounded primary-body priority audit did not authenticate an earlier explicit full-six-coefficient diagnosis, but historical firstness and guaranteed novelty are not established. Unread primary bodies and version limits are disclosed. No unprinted repaired finite-genus or approximateProblem2B solution is claimed. The deposit includes the self-contained note, standalone LaTeX source, exact-rational polynomial and universal quadratic-bound controls with ordinary/optimized reproduction, and source-audit materials. AI tools were used extensively in development, drafting, sourcing, reproduction and adversarial review. This preprint is unrefereed and has not undergone conventional human peer review.
Authors
- Kriebel Alec (ORCID: https://orcid.org/0009-0001-9320-500X)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-13
- DOI
- https://doi.org/10.5281/zenodo.23355941
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- preprint