{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:vinzant-phase-retrieval-injectivity",
  "title": "Vinzant's Conjecture on Phase Retrieval Injectivity",
  "canonical_statement": "Vinzant conjectured, in a form later restated by Bandeira, that the $4M-4$ threshold for injective complex phase retrieval is sharp. Part (1) holds: for $A \\in \\mathbb{C}^{N \\times M}$ with $N = 4M-5$ and i.i.d. standard complex Gaussian entries, the phase retrieval map generated by $A$ fails to be injective with positive probability.",
  "plain_summary": "VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "partial",
  "solution_events": [
    {
      "id": "vibemathed:vinzant-phase-retrieval-injectivity:event",
      "problem_id": "vibemathed:vinzant-phase-retrieval-injectivity",
      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-06-16T00:00:00.000Z",
      "title": "arXiv:2606.17922 - On Injectivity of Phase Retrieval",
      "summary": "part (1) of the conjecture",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:vinzant-phase-retrieval-injectivity:attempt"
      ],
      "method_family_ids": [
        "vibemathed:vinzant-phase-retrieval-injectivity:method"
      ],
      "source_assertion_ids": [
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      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:vinzant-phase-retrieval-injectivity:attempt",
      "problem_id": "vibemathed:vinzant-phase-retrieval-injectivity",
      "model": "Rethlas",
      "provider": null,
      "attempted_at": "2026-06-16T00:00:00.000Z",
      "human_collaborators": [
        "Zhangsong Li"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The paper states that the main result was obtained using generative AI, in particular the Rethlas system.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2606.17922 - On Injectivity of Phase Retrieval",
          "url": "https://arxiv.org/abs/2606.17922",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Vinzant's Conjecture on Phase Retrieval Injectivity",
          "url": "https://vibemathed.com/problem/vinzant-phase-retrieval-injectivity",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:vinzant-phase-retrieval-injectivity:verification",
      "problem_id": "vibemathed:vinzant-phase-retrieval-injectivity",
      "solution_event_id": "vibemathed:vinzant-phase-retrieval-injectivity:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Short single-author arXiv note; not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: Vinzant's Conjecture on Phase Retrieval Injectivity",
          "url": "https://vibemathed.com/problem/vinzant-phase-retrieval-injectivity",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2606.17922 - On Injectivity of Phase Retrieval",
          "url": "https://arxiv.org/abs/2606.17922",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv:2606.17922 - On Injectivity of Phase Retrieval",
      "url": "https://arxiv.org/abs/2606.17922",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Vinzant's Conjecture on Phase Retrieval Injectivity",
      "url": "https://vibemathed.com/problem/vinzant-phase-retrieval-injectivity",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "expand",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:vinzant-phase-retrieval-injectivity:signal:recent_partial_result",
      "problem_id": "vibemathed:vinzant-phase-retrieval-injectivity",
      "kind": "recent_partial_result",
      "reason": "A source-reported partial result may support bounded expansion.",
      "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"
}