{"id":"openai-math/The-Artinian-Lex-Plus-Powers-Betti-Theorem","pdf":"https://github.com/openai/math/blob/main/preprints/The-Artinian-Lex-Plus-Powers-Betti-Theorem-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Artinian-Lex-Plus-Powers-Betti-Theorem-September-23-2026","tags":["commutative-algebra","betti-numbers","lex-plus-powers"],"score":0,"title":"The Artinian Lex-Plus-Powers Betti Theorem","domain":"Algebra","family":"200","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Eisenbud–Green–Harris and lex-plus-powers"}