What question did this study set out to answer?

This work aims to correct and classify rational-derived quartics while addressing gaps in the existing proofs.

August 6, 2026Open Access

Rational-derived quartics in Lean: a corrected repeated-root classification and the boundary of Conjecture 1

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Three-part study repairs and clarifies the classification of rational-derived quartics, suggesting implications for Conjecture 1.

This work aims to correct and classify rational-derived quartics while addressing gaps in the existing proofs.
Formalized a three-part study in Lean 4 focusing on the classification of rational-derived quartics.
Identified and corrected circular reasoning and gaps in Buchholz and MacDougall's Theorem 7.
Developed a new theorem (Theorem 7′) to classify repeated-root quartics without rank computations.
Corrected Theorem 7's circularity and applied a rank-free classification for repeated-root quartics.
Established the normalised connection between Conjecture 1 and the existence of rational points on a splitting surface.
Confirmed the nonexistence of nontrivial rational points, contributing new insights into Conjecture 1's boundary.

Hiroki Fukui (2026) studied this question.

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