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  "problem_id": "vibemathed:tsp-optimal-chain-density",
  "title": "Optimal Chain Density and Space-Time Tradeoffs for the TSP",
  "canonical_statement": "The paper nearly settles the tradeoff between the size of a set system over $[n]$ and its number of full chains, an extremal question raised by Johnson, Leader and Russell as a counterpart to Sperner-type results, and linked by recent work to the space and time complexity of Bellman–Held–Karp dynamic programming for permutation problems.",
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      "title": "arXiv",
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          "url": "https://arxiv.org/abs/2607.11311",
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}