Breakthrough Tracker record

A preprint claims Mond’s conjecture for corank-one maps from C³ to C⁴

Rimányi claims that every Aₑ-finite corank-one map germ from C³ to C⁴ satisfies the Mond inequality between Aₑ-codimension and image Milnor number, with equality for quasihomogeneous germs.

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Stable ID: math-mond-corank-one-three-four-2026
Revision: math-mond-corank-one-three-four-2026.v1
Field: Mathematics · Singularity theory and complex analytic map germs
Evidence: Tier 1 · Peer reviewed: No
Record state: Provisional · Provisional partial-case proof
Last checked: 2026-10-05

AI role

The manuscript reports that Claude and ChatGPT materially assisted computer experiments, first drafts of several proofs and internal audits; the author retains responsibility.

Record details

Problem or result: The corank-one C³-to-C⁴ case of Mond’s conjecture
Authors: Richárd Rimányi
Institutions: No institution was stated in the inspected manuscript author block
Result date: First-version preprint submitted October 2, 2026

Why it matters

The paper claims the first broad three-dimensional corank-one case after more than thirty years of partial results.

Limits

This is a primary-only, unrefereed first version without a formal artifact or independent proof assessment. It covers the corank-one C³-to-C⁴ case, not the full conjecture in higher dimensions, and reduces further cases to another inequality.

Sources

Primary: Rimányi, Mond’s conjecture for corank-one maps C³ to C⁴

Correction and revision history

2026-10-05 — Added after primary-source, scope, status, AI-role and limitation review.

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