Breakthrough Tracker record

A preprint claims a complete, Lean-formalized solution to Colombo’s determinant problem

Qianli Ma proves a necessary-and-sufficient condition for the determinant of the matrix with entries (x_j−x_i)^D to be nonzero for distinct real nodes, completing Colombo’s 1928 problem. The new odd-exponent branch is accompanied by a Lean 4 formalization.

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Stable ID
math-colombo-determinant-problem-solution-2026
Revision
math-colombo-determinant-problem-solution-2026.v1
Field
Mathematics · Analysis, determinant inequalities and formalized mathematics
Evidence
Tier 1 · Peer reviewed: No
Record state
Provisional · Provisional Lean-formalized claimed solution
Last checked

AI role

The author reports substantial use of WuJie and other AI agents plus DeepSeek, Qwen, Kimi and GPT to identify the strategy and draft the proof. The author checked and revised the argument, formalized it in Lean 4 and accepts responsibility.

Record details

Problem or result
Colombo’s 1928 determinant nonvanishing classification for powers of pairwise differences
Authors
Qianli Ma
Institutions
Zhejiang University; WuJie AI
Result date
First-version preprint submitted August 31, 2026

Why it matters

The result supplies the missing odd-exponent classification for a problem originating in hyperbolic partial differential equations. The independent odd-branch preprint and Lean artifact provide stronger corroboration than an isolated informal claim.

Limits

The complete classification remains a non-peer-reviewed preprint. The repository reports a pinned Lean 4.30/mathlib build with 2,817 jobs and no sorry/admit declarations, but this cycle reviewed the artifact metadata and source rather than independently rebuilding the full formalization.

Sources

  1. Primary: Ma, claimed solution to Colombo’s determinant problem
  2. Artifacts: Lean 4 formalization of the odd-exponent branch
  3. Independent: Independent proof of the odd-exponent branch

Correction and revision history

  1. 2026-09-04 — Added after primary-source, scope, status, AI-role and limitation review.

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