The Ellipsoid Fitting Conjecture
Statement
Given n independent standard Gaussian vectors in R^d, an ellipsoid fit is a positive semidefinite S with x_i' S x_i = d for every i. Saunderson, Parrilo and Willsky conjectured that this semidefinite feasibility problem has a sharp threshold at n ~ d^2/4. Proved: below the threshold a fit exists with probability tending to one, above it none does.
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No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Theodor Misiakiewicz and Garrett G. Wen, using GPT-5.6That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The approach is the authors' own - they say so, and trace it to the dual formulation of Bandeira and Maillard. What the model did is named step by step: ChatGPT 5.4 and 5.5 were used "to explore several possible proof strategies", and then, "Given an earlier draft, GPT 5.6 helped repair and complete several arguments, including the tightened head-tail decomposition in Lemma 3.5 and the decomposition used in the proof of Proposition 4.4, which ultimately led to the completion of the proofs."
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