{
  "subject": "Erdős Problems 552 and 85: Chen bound (formalized), equivalence, corrections",
  "claims": [
    {
      "id": "E1",
      "claim": "R(C4,K_{1,n+1}) <= R(C4,K_{1,n}) + 2 for n >= 1 (Chen 1997)",
      "type": "formally verified (Lean 4 kernel)",
      "evidence": "lean/Erdos/Erdos552.lean, agnt-gg/erdos-lean 8e5972f4e6787049b168e5350b1a2badc9eb8bcd; axioms propext, Classical.choice, Quot.sound; fails without n >= 1 (negative control)"
    },
    {
      "id": "E2",
      "claim": "f85(n) = min{k : R(C4,K_{1,n-k}) <= n}; the erdosproblems.com formula min{m : m >= R(C4,K_{1,n-m})} is wrong",
      "type": "proved; brute force on all graphs with <= 7 vertices",
      "evidence": "battery_552.py and output (f85(4..7) = 2,3,3,3)"
    },
    {
      "id": "E3",
      "claim": "Problem 85 holds iff R(C4,K_{1,s+1}) = R(C4,K_{1,s}) for only finitely many s",
      "type": "proved (informal); consistent with all 38 known values",
      "evidence": "paper section 3; f85_from_ramsey.py and output"
    },
    {
      "id": "E4",
      "claim": "f85(15) >= 5 > sqrt(15) + 1, refuting f(n) < sqrt(n) + 1 on the problem page",
      "type": "explicit witness, verified twice (z3 and plain Python)",
      "evidence": "witness_f85.py, witness_n15_k4.json, witness_f85_output.txt"
    },
    {
      "id": "E5",
      "claim": "Problem 552 has a $100 prize; the community database listed none",
      "type": "record correction",
      "evidence": "teorth/erdosproblems pull request 456"
    }
  ],
  "submissions": [
    "https://github.com/google-deepmind/formal-conjectures/pull/6904",
    "https://github.com/teorth/erdosproblems/pull/456",
    "https://github.com/teorth/erdosproblems/issues/457"
  ],
  "open": [
    "Problem 552 main question",
    "Problem 85 (equivalently: finitely many plateaus of R(C4,K_{1,s}))"
  ]
}