{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1151",
  "content_hash": null,
  "slug": "space-curves-set-theoretic-complete-intersection-attempt-resolution-route",
  "type": "attempt",
  "title": "Resolve the stated acceptance condition",
  "summary": "Prove that every irreducible curve \\(C\\subset\\mathbb P^3_{\\mathbb C}\\) is the set-theoretic intersection of two surfaces, with no degree restriction.",
  "relevance": "For Set-theoretic complete intersections for complex space curves, record space-curves-set-theoretic-complete-intersection-attempt-resolution-route (“Resolve the stated acceptance condition”) documents a concrete method, search boundary, or failed route. The record states: Prove that every irreducible curve \\(C\\subset\\mathbb P^3_{\\mathbb C}\\) is the set-theoretic intersection of two surfaces, with no degree restriction.",
  "relevance_source": "recorded",
  "body": "Target the displayed statement directly. Prove that every irreducible curve \\(C\\subset\\mathbb P^3_{\\mathbb C}\\) is the set-theoretic intersection of two surfaces, with no degree restriction. Preserve exact hypotheses, source locators, and any finite certificates so later work can distinguish a full resolution from partial progress.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://mathoverflow.net/questions/190938/is-every-projective-space-curve-a-set-theoretic-intersection-of-two-surfaces-wh",
      "locator": "Editorial research route recorded 2026-07-31"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/190938/is-every-projective-space-curve-a-set-theoretic-intersection-of-two-surfaces-wh",
    "locator": "Editorial research route recorded 2026-07-31"
  },
  "relations": [
    {
      "slug": "R1152",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "space-curves-set-theoretic-complete-intersection",
      "title": "space curves set theoretic complete intersection",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}