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The Divisible Rank-Three Case of the Kajitani–Ueno–Miyano Conjecture
Proves the divisible rank-three case: rank exactly three and ground-set size a multiple of three, with no restriction to simple, paving, representable or graphic matroids. The part not previously in the literature is the non-simple sub-case, since McGuinness had settled all paving matroids and a rank-three matroid is paving exactly when it has no parallel pairs. Combined with the coprime-case theorem of van den Heuvel and Thomasse, this covers every finite uniformly dense rank-three matroid. The conjecture remains open in higher rank.
Exact FrontierDelta
proved→proved
Scope and record
Occurred: Oct 29, 2026
Delta type: REGISTRY REVISION
Assumptions: VibeMathed verification: lean-verified. 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: The Divisible Rank-Three Case of the Kajitani–Ueno–Miyano Conjecture · Divisible rank-three KUM
Confidence: Not scored
Registry verification: lean verified · preprint · partial
Attribution
VibeMathed
registry · event recorded by
GPT-5.6 Sol
model · ai model contributor · OpenAI
Claude Opus 5 (for some Lean formalization and paper write-up)
model · ai model contributor · Anthropic
Compute record
No linked compute attempts recorded.
Lineage and corrections
Corrects The Divisible Rank-Three Case of the Kajitani–Ueno–Miyano Conjecture →
Supersedes The Divisible Rank-Three Case of the Kajitani–Ueno–Miyano Conjecture →
Lean repo evidence for this event
VibeMathed record: The Divisible Rank-Three Case of the Kajitani–Ueno–Miyano Conjecture evidence for this event
Archived repo evidence for this event
This event attributed to Claude Opus 5 (for some Lean formalization and paper write-up)
The Divisible Rank-Three Case of the Kajitani–Ueno–Miyano Conjecture parent of this event
The Divisible Rank-Three Case of the Kajitani–Ueno–Miyano Conjecture evidence for this event
This event attributed to GPT-5.6 Sol
Proves the divisible rank-three case: rank exactly three and ground-set size a multiple of three, with no restriction to simple, paving, representable or graphic matroids. The part not previously in the literature is the non-simple sub-case, since McGuinness had settled all paving matroids and a rank-three matroid is paving exactly when it has no parallel pairs. Combined with the coprime-case theorem of van den Heuvel and Thomasse, this covers every finite uniformly dense rank-three matroid. The conjecture remains open in higher rank. parent of this event
Act on this frontier