The Hall-Ho Heat Flow Conjecture for Random Matrices
Hall and Ho conjectured how the zeros of the heat-flow-evolved characteristic polynomial of a random matrix behave in the large- limit. General cases are proved; in particular, for a complex Ginibre matrix the empirical measure of those zeros converges almost surely to the semicircle law.
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Random matrix theory
- Posed by
- Brian Hall, Ching-Wei Ho
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-27
- Model
- ChatGPT Pro 5.5, ChatGPT 5.6 Sol Ultra
- Vendor
- OpenAI
- Collaborators
- Theodoros Assiotis
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
Proves general cases of the conjecture rather than every case.
What the AI did
An unusually direct disclosure: "In the course of the research presented here I have been using AI tools extensively, most significantly ChatGPT Pro 5.5 and ChatGPT 5.6 Sol Ultra for ideation, technical help, editing and checking the proofs and general editing and proofreading of the manuscript, at the level of a co-author. All mistakes are my own responsibility." The phrase "at the level of a co-author" is the author's own.
Verification
A preprint, with no independent review.