Seymour's Second Neighborhood Conjecture
A dense case, not the conjecture: it remains open in general. The concrete gain is on the size of any counterexample - combined with the known minimum-outdegree results, this raises the best known lower bound on the order of a counterexample from 16 to 17, and to 19 conditional on the 2026 preprint of Sadhukhan, Sandeep and Sen. The novelty against the earlier dense-case work is that no structure is prescribed on the missing edges. Superseded by a claimed proof of the full conjecture in the OpenAI math release (September 2026), see seymour-second-neighborhood-conjecture.
Exact FrontierDelta
Scope and record
Occurred: Oct 29, 2026
Delta type: REGISTRY REVISION
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. 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: Seymour's Second Neighborhood Conjecture · Seymour 2nd neighborhood
Confidence: Not scored
Registry verification: unreviewed · preprint · partial
Attribution
VibeMathed
registry · event recorded by
GPT-5 family
model · ai model contributor · OpenAI
Claude
model · ai model contributor · Anthropic
Jake Brukhman
human · human collaborator
Lineage and corrections
Corrects Seymour's Second Neighborhood Conjecture →
Supersedes Seymour's Second Neighborhood Conjecture →
This event attributed to GPT-5 family
This event attributed to Jake Brukhman
This event attributed to Claude
A dense case, not the conjecture: it remains open in general. The concrete gain is on the size of any counterexample - combined with the known minimum-outdegree results, this raises the best known lower bound on the order of a counterexample from 16 to 17, and to 19 conditional on the 2026 preprint of Sadhukhan, Sandeep and Sen. The novelty against the earlier dense-case work is that no structure is prescribed on the missing edges. Superseded by a claimed proof of the full conjecture in the OpenAI math release (September 2026), see seymour-second-neighborhood-conjecture. parent of this event
Stronger result in the OpenAI math release evidence for this event
Seymour's Second Neighborhood Conjecture evidence for this event
VibeMathed record: Seymour's Second Neighborhood Conjecture evidence for this event
Seymour's Second Neighborhood Conjecture parent of this event
Act on this frontier