What was already known
Vinzant disproved an earlier 4M−4 necessity conjecture with an injective 11-measurement construction in C⁴. The refined random-matrix conjecture’s p_M<1 part was known only for M=2 and M=2^k+1.
AI involvement
Zhangsong Li says Rethlas produced the main result after receiving only the conjecture, without further mathematical input. Li verified the proofs and edited and reorganized the manuscript.
The v1 disclosure says the main result was obtained by simply prompting Rethlas with the conjecture, without additional mathematical input, before Li's checking and editing.
Importance
Settles the all-dimensions noninjectivity part of Vinzant’s refined conjecture.
Limitations
The separate limit claim p_M→0 is not proved. Li reports checking the generated proof but provides no separate review log.
Technical verification
The named human author explicitly reports verifying the generated proofs of the assessed theorem. This is source-reported complete human proof checking; no machine formalization or independent reproduction is claimed.
Formal checking
Human verification of Rethlas-generated proofs before editing and reorganizing the manuscript
- Checker
- Zhangsong Li, manuscript author
- Scope
- Theorem 1.2, the nonempty open set of noninjective complex phase-retrieval matrices for every M>=2 and N=4M-5
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Li reorganized and explains the central mechanism in §2: a rank-two Hermitian kernel witness at an explicit matrix and persistence of that witness on an open neighborhood by the implicit function theorem.
Correction and publication history
Settles the all-dimensions noninjectivity part of Vinzant’s refined conjecture.
Read this published revision