The Nagata conjecture for plane curves predicts the strict degree-multiplicity inequality
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for a nonzero effective complex projective plane curve of degree 
at 
very general distinct points with prescribed nonnegative integer multiplicities 
no larger than the actual multiplicities. Repeated or reducible
components and unequal multiplicities are allowed. Very general means outside a countable
union of proper Zariski-closed subsets of the ordered configuration space.
Tevelev (2026) gives an expanded human exposition of a proof attributed to OpenAI. His stated theorem treats the equal-multiplicity case: a degree-
plane curve with multiplicity
at least 
at 
very general points satisfies 
. The notes explain
the argument rather than claim a new proof. This reference does not by itself verify
every companion claim in the original announcement, including the higher-dimensional
statements about Seshadri constants.
Bruce (2026, Theorem D) reports a proof of the strict inequality for every 
at very general points of 
. The argument uses degeneration to a nodal curve
and interpolation of Laurent polynomials, giving
a tropical reworking of earlier AI-generated arguments.
