Problem detail · source-aware
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Can the $k$-distinct language - words over $[n]$ of length at most $k$ with no repeated symbol - be recognized by an acyclic NFA of size $c^k n^{O(1)}$ for some $c < 4$? A construction of size $2^{1.96992k} n^{O(1)} < 3.918^k n^{O(1)}$ answers yes.
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 gadget-amplification framework - hashing symbols into many copies of a small local NFA gadget - was developed across ChatGPT/Codex 5.4-5.6 Pro and Gemini 3.1 Pro sessions.
Provider: OpenAI / Google DeepMind · Prompt public: unknown · Independence: unknown
arXiv preprint with interval-arithmetic verification of the exponent and pinned verification code. Not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.