{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:matrix-spencer-group-version",
  "title": "The Matrix Spencer Conjecture for Finite Groups",
  "canonical_statement": "The group version of the Matrix Spencer conjecture holds: for every finite group $G$ there are signs $\\varepsilon \\in \\{\\pm 1\\}^G$ with $\\left\\|\\sum_{g \\in G} \\varepsilon_g \\rho(g)\\right\\| \\le C\\sqrt{|G|}$, where $\\rho$ is the left regular representation and $C$ is universal.",
  "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:matrix-spencer-group-version:event",
      "problem_id": "vibemathed:matrix-spencer-group-version",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-06-10T00:00:00.000Z",
      "title": "arXiv:2606.12181 - Matrix Discrepancy for Representations of Finite Groups",
      "summary": "the group case; the full Matrix Spencer conjecture remains open",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:matrix-spencer-group-version:attempt"
      ],
      "method_family_ids": [
        "vibemathed:matrix-spencer-group-version:method"
      ],
      "source_assertion_ids": [
        "vibemathed:matrix-spencer-group-version:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:matrix-spencer-group-version:attempt",
      "problem_id": "vibemathed:matrix-spencer-group-version",
      "model": "ChatGPT Pro 5.5, Claude Opus 4.7 and 4.8",
      "provider": "OpenAI / Anthropic",
      "attempted_at": "2026-06-10T00:00:00.000Z",
      "human_collaborators": [
        "Afonso S. Bandeira",
        "Helmut Bolcskei"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The acknowledgement says modern AI tools were used throughout, and singles out one of the key arguments as the one that broke the problem open, crediting it to that use.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "A structured special case proved independently the same week, arXiv:2606.16005",
          "url": "https://arxiv.org/abs/2606.16005",
          "kind": "independent",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "arXiv:2606.12181 - Matrix Discrepancy for Representations of Finite Groups",
          "url": "https://arxiv.org/abs/2606.12181",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Matrix Spencer Conjecture for Finite Groups",
          "url": "https://vibemathed.com/problem/matrix-spencer-group-version",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:matrix-spencer-group-version:verification",
      "problem_id": "vibemathed:matrix-spencer-group-version",
      "solution_event_id": "vibemathed:matrix-spencer-group-version:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "arXiv preprint; not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: The Matrix Spencer Conjecture for Finite Groups",
          "url": "https://vibemathed.com/problem/matrix-spencer-group-version",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2606.12181 - Matrix Discrepancy for Representations of Finite Groups",
          "url": "https://arxiv.org/abs/2606.12181",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv:2606.12181 - Matrix Discrepancy for Representations of Finite Groups",
      "url": "https://arxiv.org/abs/2606.12181",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Matrix Spencer Conjecture for Finite Groups",
      "url": "https://vibemathed.com/problem/matrix-spencer-group-version",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:matrix-spencer-group-version:signal:watch_only",
      "problem_id": "vibemathed:matrix-spencer-group-version",
      "kind": "watch_only",
      "reason": "Current public evidence does not meet the default replay threshold.",
      "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"
}