VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Given $n$ independent standard Gaussian vectors in $\mathbb{R}^d$, an ellipsoid fit is a positive semidefinite matrix $S$ 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 $n \sim \frac{d^2}{4}$. Proved: below the threshold a fit exists with probability tending to one, above it none does.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
GPT-5.6
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."
Closes both gaps left open by Bandeira and Maillard: exact fitting, and removal of the operator-norm constraint. The threshold turns out to be governed by the statistical dimension d(d+1)/4 of the PSD cone.
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.