Eisenbud–Green–Harris and lex-plus-powers

What OpenAI claims

Proves the Eisenbud–Green–Harris and lex-plus-powers conjectures over every characteristic-zero field. Any homogeneous ideal containing a regular sequence, of arbitrary length and degrees at least two, admits a lex-plus-powers ideal with the same Hilbert function and no smaller graded Betti numbers.

Papers (2)

1. The Artinian Lex-Plus-Powers Betti Theorem

   23 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract We prove the Eisenbud–Green–Harris and lex-plus-powers conjectures over every characteristic-zero field for homogeneous regular sequences of any positive length, with degrees at least two. For every homogeneous ideal containing such a sequence, the corresponding lex-plus-powers ideal has the same Hilbert function and at least as large a graded Betti number in every homological and internal degree.

2. Commuting Division-Coefficient Forms and the Artinian Eisenbud--Green--Harris Conjecture

   23 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract We prove the Eisenbud–Green–Harris conjecture over every characteristic-zero field for homogeneous regular sequences of any positive length, with degrees at least two. Thus every homogeneous ideal containing such a sequence has the Hilbert function of a monomial ideal containing the corresponding pure powers.

Status

Preprint. The papers have not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.