Source authenticated

The lex-plus-powers conjecture over fields of characteristic zero

Claims the lex-plus-powers conjecture over every characteristic-zero field, for regular sequences of any length with degrees at least two and no growth condition, with no restriction on the other generators of $I$ ; this contains the Eisenbud-Green-Harris statement. The key new step is a Hilbert-matching monomial ideal with no smaller Betti numbers (Mermin-Murai Conjecture 10.2). It does NOT treat positive characteristic.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The lex-plus-powers conjecture over fields of characteristic zero · Lex-plus-powers conjecture (char. 0)

Confidence: Not scored

Registry verification: unreviewed · announcement · partial

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Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

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Named evidence

VibeMathed record: The lex-plus-powers conjecture over fields of characteristic zero

specialist registry · passed

No independent mathematician has checked this yet. Theorem 1.1 (Artinian, over $\mathbb C$ ) and Corollary 1.2 (every characteristic-zero field, regular sequences of any length) were read against the conjecture: the lex-plus-powers ideal exists, has the same Hilbert function and has graded Betti numbers at least those of $S/I$ in every homological and internal degree. The non-Artinian case uses the published Caviglia-Kummini reduction. Positive characteristic is not addressed. No Lean formalization.

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The lex-plus-powers conjecture over fields of characteristic zero

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Companion: Commuting Division-Coefficient Forms and the Artinian Eisenbud-Green-Harris Conjecture

paper · pending

paper link supplied by the VibeMathed registry.

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This event attributed to Unreleased internal OpenAI model

The lex-plus-powers conjecture over fields of characteristic zero parent of this event

VibeMathed record: The lex-plus-powers conjecture over fields of characteristic zero evidence for this event

The lex-plus-powers conjecture over fields of characteristic zero evidence for this event

Companion: Commuting Division-Coefficient Forms and the Artinian Eisenbud-Green-Harris Conjecture evidence for this event

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