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

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
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preprint

No open exact-root cover for Vassiliev's quadratic family

Kriebel Alec
Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
preprint

No open exact-root cover for Vassiliev's quadratic family

Kriebel Alec
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
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