{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:anderson-quasi-completeness",
  "title": "Anderson's Quasi-Completeness Question",
  "canonical_statement": "Is every weakly quasi-complete Noetherian local ring quasi-complete? Asked by D. D. Anderson in 2014. The ring $A = k^p[[X, Y]][k]$ with $k = \\mathbb{F}_p(u_1, u_2, \\dots)$ is weakly quasi-complete but not quasi-complete.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "resolved",
  "solution_events": [
    {
      "id": "vibemathed:anderson-quasi-completeness:event",
      "problem_id": "vibemathed:anderson-quasi-completeness",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-04-04T00:00:00.000Z",
      "title": "arXiv:2604.03789 - Automated conjecture resolution with formal verification",
      "summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:anderson-quasi-completeness:attempt"
      ],
      "method_family_ids": [
        "vibemathed:anderson-quasi-completeness:method"
      ],
      "source_assertion_ids": [
        "vibemathed:anderson-quasi-completeness:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:anderson-quasi-completeness:attempt",
      "problem_id": "vibemathed:anderson-quasi-completeness",
      "model": "Rethlas + Archon (GPT-5.4 Pro)",
      "provider": "OpenAI",
      "attempted_at": "2026-04-04T00:00:00.000Z",
      "human_collaborators": [],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The dual-agent framework (Rethlas for informal reasoning, Archon for formal verification) ran roughly 80 hours; the decisive example is a classical ring going back to Nagata, which the system recognized as answering Anderson's question.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2604.03789 - Automated conjecture resolution with formal verification",
          "url": "https://arxiv.org/abs/2604.03789",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Anderson's Quasi-Completeness Question",
          "url": "https://vibemathed.com/problem/anderson-quasi-completeness",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:anderson-quasi-completeness:verification",
      "problem_id": "vibemathed:anderson-quasi-completeness",
      "solution_event_id": "vibemathed:anderson-quasi-completeness:event",
      "level": "lean_verified_statement_audited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "audited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Lean-checked with a statement comparator guarding against misformalization; arXiv preprint documents the pipeline.",
      "sources": [
        {
          "label": "VibeMathed: Anderson's Quasi-Completeness Question",
          "url": "https://vibemathed.com/problem/anderson-quasi-completeness",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2604.03789 - Automated conjecture resolution with formal verification",
          "url": "https://arxiv.org/abs/2604.03789",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv:2604.03789 - Automated conjecture resolution with formal verification",
      "url": "https://arxiv.org/abs/2604.03789",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Anderson's Quasi-Completeness Question",
      "url": "https://vibemathed.com/problem/anderson-quasi-completeness",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "replay",
  "recommended_exposure": "method_aware",
  "opportunity_signals": [
    {
      "id": "vibemathed:anderson-quasi-completeness:signal:replay_ready",
      "problem_id": "vibemathed:anderson-quasi-completeness",
      "kind": "replay_ready",
      "reason": "A public source and a non-unreviewed verification label support replay triage.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
    "VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}