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”OpenAI's GPT-5.6 Sol”か

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Square Functions and the Complete Crouzeix Conjecture in Dimension Three
AI による概要
The complete Crouzeix's conjecture is settled for matrices of order up to three, alongside sharp column and row square-function inequalities, in recent work detailed in Square Functions and the Complete Crouzeix Conjecture in Dimension Three.
https://papers.cool/arxiv/2608.27346 Publish: 2026-08-27

Overview of the Result
・ The complete conjecture is now proven to hold for any \(3 \times 3\) complex matrix, expanding past previous partial results that required special structures like tridiagonal forms or central eigenvalues.
https://arxiv.org/html/1707.08603v2
arXiv:1707.08603v2 [math.NA] 21 Nov 2017
Some Extensions of the Crouzeix-Palencia Result Trevor Caldwell, Anne Greenbaum, Kenan Li
・ Sharp inequalities for both row and column square-functions are established as key tools in resolving the bound at this dimension.
・The Conjecture: Michel Crouzeix originally proposed in 2004 that \(\Vert{}p(A)\Vert{} \le 2 \max_{z \in W(A)} \vert{}p(z)\vert{}\) for any polynomial \(p\) and square matrix \(A\), where \(W(A)\) is the numerical range.
ResearchGate https://www.researchgate.net/publication/411306471_A_solution_to_Crouzeix's_conjecture

If you would like, I can provide:
More details on the square-function inequalities used in the proof
Background on earlier partial bounds like the \(1+\sqrt{2}\) constant
Let me know what aspect you wish to explore.

https://en.wikipedia.org/wiki/Crouzeix%27s_conjecture
Crouzeix's conjecture
Claimed proof
On July 27, 2026, neurosurgeon Shanmu Jin posted a preprint claiming a proof of Crouzeix's conjecture.[9] Jin reported that the proof was obtained with the assistance of OpenAI's GPT-5.6 Sol model during an approximately sixteen-hour autonomous reasoning session in ChatGPT Work, ・・