Problem detail · source-aware
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A $t$-$(v,k,\lambda)$ covering is a family of $k$-subsets of a $v$-set meeting every $t$-subset at least $\lambda$ times, and $C(v,k,t)$ is the least number of blocks. The recorded bounds for $C(12,6,4)$ were $40 \le C(12,6,4) \le 41$. No $4$-$(12,6,1)$ covering with $40$ blocks exists, so $C(12,6,4) = 41$.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
The disclosure lists exploratory analysis, computational search, supporting code, manuscript drafting and revision, and proofreading, without separating which step came from where, so the lowest tier applies.
Provider: OpenAI / Anthropic · Prompt public: unknown · Independence: unknown
The non-existence argument is a forced-structure search: a counting argument pins every point to degree exactly 20 and forces each point link to be an optimal 3-(11,5,1) covering, collapsing the search space. Single-author arXiv preprint, not peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
closes a one-block gap in the covering tables; the analogous next case is not reachable by this method
Source-reported tools: computation.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.