Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 200-01. The Artinian Lex-Plus-Powers Betti Theorem
Manuscript map · lines 5975–5984
OpenAI@2026-10-07#rem:oai-p-200-01
Authors: OpenAI. Family 200.
Title: The Artinian Lex-Plus-Powers Betti Theorem.
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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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