What was already known
The 1/4 threshold was conjectured by Saunderson, Parrilo and Willsky. Earlier work proved approximate fitting under an operator-norm constraint, leaving exact fitting and the unrestricted no-fit side open.
AI involvement
Misiakiewicz and Wen say they supplied the approach, motivated by earlier duality and Gaussian equivalence. Given their draft, GPT-5.6 repaired and completed Lemma 3.5 and the decomposition in Proposition 4.4, both used to finish the proofs. The model did not originate the overall Gaussian-comparison program.
The disclosed model-generated decompositions repair load-bearing mathematical steps in both sides of the threshold proof, within a human-designed approach.
Importance
Establishes the proposed sharp threshold for exact random ellipsoid fitting.
Limitations
The authors designed the Gaussian-comparison approach; GPT-5.6 repaired load-bearing steps in both phases. The rowwise extension in Proposition 4.8 is sketched, with its uniformity assumptions flagged in an AI review.
Technical verification
The two human authors explicitly report careful verification of all results. This is a reported author check, not an independent audit or machine formalization. Proposition 4.8's rowwise extension is only sketched in the manuscript, leaving an exposition gap to follow.
Formal checking
Careful author verification of all results
- Checker
- Theodor Misiakiewicz and Garrett G. Wen, paper authors
- Scope
- Sharp SAT and UNSAT phases in Theorem 1.2, including Lemma 3.5 and Proposition 4.4
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the sparse-head correction, low-influence Gaussian comparison, spectral-head/diffuse-bulk split and projected Gordon argument.
Correction and publication history
Establishes the proposed sharp threshold for exact random ellipsoid fitting.
Read this published revision