{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1646",
  "content_hash": null,
  "slug": "matrix-spencer-discrepancy-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: The conjectured bound holds for commuting matrices and for matrices of rank at most \\(n/\\log^3 n\\); general concentration gives an extra \\(\\sqrt{\\log n}\\) factor. Exact unresolved remainder: Remove the logarithmic loss without rank or commutativity hypotheses.",
  "relevance": "This is the dated publication status for the canonical target Matrix Spencer discrepancy conjecture.",
  "relevance_source": "recorded",
  "body": "The problem was checked as open on 2026-08-01.\n\nThe strongest neighboring result found in the cited sources is: The conjectured bound holds for commuting matrices and for matrices of rank at most \\(n/\\log^3 n\\); general concentration gives an extra \\(\\sqrt{\\log n}\\) factor.\n\nThe exact unresolved remainder is: Remove the logarithmic loss without rank or commutativity hypotheses.\n\nA complete resolution must meet the following acceptance conditions:\n- Prove the bound with one universal \\(C\\), or give a family for which the minimum signed-sum norm divided by \\(\\sqrt n\\) is unbounded.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.48550/arXiv.2504.20539",
      "locator": "Afonso S. Bandeira, Anastasia Kireeva, Antoine Maillard, and Almut Rödder, “Randomstrasse101: Open Problems of 2024,” arXiv:2504.20539, version dated 22 March 2026. Conjecture 1 and 2026 update record"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.48550/arXiv.2504.20539",
    "locator": "Afonso S. Bandeira, Anastasia Kireeva, Antoine Maillard, and Almut Rödder, “Randomstrasse101: Open Problems of 2024,” arXiv:2504.20539, version dated 22 March 2026. Conjecture 1 and 2026 update record"
  },
  "relations": [
    {
      "slug": "R1645",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1643",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1644",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "matrix-spencer-discrepancy",
      "title": "matrix spencer discrepancy",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}