{
  "schema_version": "1.0",
  "assignment": "Prove all-index coefficient nonnegativity from the exact degree-weighted recurrence, c(0)=1 and nonnegative weights. No finite cutoff or added hypotheses.",
  "roles": [
    "lean_worker",
    "research_coordinator"
  ],
  "delivered_theorem": "OrchardMath.Millennium.HardyRecurrence.coefficients_nonneg",
  "source_sha256": "66b5123294fac69e634751d8c16bdbbfe8f967f66f0111a797a6f4c9e372427c",
  "worker_compile_attempts": 2,
  "worker_failed_candidates": 0,
  "attempt_detail": "The first attempt compiled with two style warnings; the second removed them. No failed proof candidate is claimed.",
  "root_validation": [
    "Read complete source and exact index box",
    "Checked strict predecessor degree decrease",
    "Fresh targeted Lake build",
    "External restatement spelling out degree, full box and pointwise subtraction",
    "Direct axiom audit"
  ],
  "axioms": [
    "propext",
    "Classical.choice",
    "Quot.sound"
  ],
  "scope": "Conditional recurrence positivity only. The coefficients are arbitrary functions satisfying the recurrence; identification with the actual rational function and explicit weights remains outside Lean.",
  "source_record": {
    "source_path": "research/millennium/iterations/0030/recurrence-bridge-notes.md",
    "source_commit": "72fde44c1d4c227e02b8ca9166cd7db04d8e6048",
    "source_sha256": "d99bc0f1d16da70e604e3b24bf7addb44567c37b2378ac9bb593c040ea92798e"
  },
  "acceptance_record": {
    "source_path": "research/millennium/iterations/0030/acceptance.json",
    "source_commit": "72fde44c1d4c227e02b8ca9166cd7db04d8e6048",
    "source_sha256": "505ec949c4e42a4f08f9730da23e9c7b16c28d4e12b9bd785f1fa6b013adea72"
  }
}