{
  "abstract": "A formalization of sharp balanced-law robustness and stability refinements of the classical four-row permanent inequalities of Carlen-Lieb-Loss and Bristiel-Caputo. It proves the exact total-variation radius 1/24, optimal variance-deficit coefficient (1-24r)/9, complete nonnegative equality cases, sharp endpoint entropy constants, and adaptive tensorization. The explicit interior exponent is sufficient rather than optimal; at radius zero it is weaker than the classical optimal uniform exponent. Lean checks exhaustive support coverage and exact rational Gram identities.",
  "authors": [
    {
      "name": "JD Jones"
    }
  ],
  "challenge_render": {
    "artifact_path": "renders/PALOMAR-2026-10-08-000007-v1/cffd35255c4016c63a9ea8c28f9589d317e8393f56ffc917d8d16634299d3748/",
    "artifact_tree_sha256": "cffd35255c4016c63a9ea8c28f9589d317e8393f56ffc917d8d16634299d3748",
    "bwrap_source_tag": "v0.12.0",
    "entrypoint": "Challenge/index.html",
    "format": "verso-html",
    "rendered_at": "2026-10-08T20:26:17Z",
    "renderer_commit": "d4e41c1d5b0d114c4859e6e5831dc6d3ad1d0d44",
    "verso_commit": "8fc7a297f14d5adc1a551b5b4ecf283c08bd691f"
  },
  "classification": {
    "arxiv": [
      "math.CO",
      "math.PR"
    ],
    "msc2020": [
      "15A15",
      "60E15",
      "26D15"
    ]
  },
  "first_registered_on": "2026-10-08",
  "formalization": {
    "challenge_path": "FourRowChallenge.lean",
    "comparator_config_path": "comparator.json",
    "definition_names": [],
    "formalization_metadata_path": "formalization.yaml",
    "lakefile_path": "lakefile.toml",
    "lean_toolchain": "leanprover/lean4:v4.35.0-rc3",
    "permitted_axioms": [
      "propext",
      "Quot.sound",
      "Classical.choice"
    ],
    "project_dependencies": [
      {
        "name": "plausible",
        "repository": "leanprover-community/plausible",
        "revision": "fb13df72ecefd8ddbf9291021d7f33a8673eb57b"
      },
      {
        "name": "LeanSearchClient",
        "repository": "leanprover-community/LeanSearchClient",
        "revision": "29ff470276c725ae01505d55b17148c18fc7dfd3"
      },
      {
        "name": "importGraph",
        "repository": "leanprover-community/import-graph",
        "revision": "10a2cfff285e1c7c2ebc49c0ba22cab0f3c58ee5"
      },
      {
        "name": "proofwidgets",
        "repository": "leanprover-community/ProofWidgets4",
        "revision": "c643bbb3c24f8a25f9c14e3a6b1ceb13d01f3de1"
      },
      {
        "name": "aesop",
        "repository": "leanprover-community/aesop",
        "revision": "a90fbf7b02ff06a0deebf74088dff9e5fe02c9ea"
      },
      {
        "name": "Qq",
        "repository": "leanprover-community/quote4",
        "revision": "37b0ba0b26109cf9f9c541f0f9557e50cfa1a3b9"
      },
      {
        "name": "batteries",
        "repository": "leanprover-community/batteries",
        "revision": "33131f4fb10067cb3009bf4db615d9680c1ccd6b"
      },
      {
        "name": "Cli",
        "repository": "leanprover/lean4-cli",
        "revision": "843844fa601dd56767b1eb22b7ada5b64d5e567a"
      },
      {
        "name": "mathlib",
        "repository": "leanprover-community/mathlib4",
        "revision": "a98628e16c11f5167f16124105ddce53efa9bfe5"
      }
    ],
    "solution_path": "FourRowSolution.lean",
    "theorem_names": [
      "FourRowPrincipal.endpoint",
      "FourRowPrincipal.sharp_stability",
      "FourRowPrincipal.stability_optimal",
      "FourRowPrincipal.explicit_extremal_family",
      "FourRowPrincipal.radius_sharp",
      "FourRowPrincipal.endpoint_equality",
      "FourRowPrincipal.explicit_exponent",
      "FourRowPrincipal.larger_exponents",
      "FourRowPrincipal.subcritical_threshold",
      "FourRowPrincipal.entropy",
      "FourRowPrincipal.observation_contraction",
      "FourRowPrincipal.entropy_optimal",
      "FourRowPrincipal.observation_optimal",
      "FourRowPrincipal.adaptive_tensorization",
      "FourRowPrincipal.adaptive_probability",
      "FourRowPrincipal.adaptive_marginals"
    ]
  },
  "id": "PALOMAR-2026-10-08-000007",
  "preservation": {
    "archive_owner": "PalomarArchive",
    "archived_at": "2026-10-08T20:26:53Z",
    "receipt_sha256": "4aea40dd00bf73659bd47d7399ed0820dab31e3fb93e852eaf80826bce791f48",
    "repositories": [
      {
        "commit": "861abe5342847d3f32985d55403547e1832ffac4",
        "fork_repository": "PalomarArchive/JD-Jones-ASES--four-row--c4855362551d",
        "ref": "refs/tags/palomar/PALOMAR-2026-10-08-000007-v1/861abe5342847d3f32985d55403547e1832ffac4",
        "source_repository": "JD-Jones-ASES/four-row"
      },
      {
        "commit": "a90fbf7b02ff06a0deebf74088dff9e5fe02c9ea",
        "fork_repository": "PalomarArchive/leanprover-community--aesop--01b46b609077",
        "ref": "refs/tags/palomar/PALOMAR-2026-10-08-000007-v1/a90fbf7b02ff06a0deebf74088dff9e5fe02c9ea",
        "source_repository": "leanprover-community/aesop"
      },
      {
        "commit": "33131f4fb10067cb3009bf4db615d9680c1ccd6b",
        "fork_repository": "PalomarArchive/leanprover-community--batteries--1b4c776305c9",
        "ref": "refs/tags/palomar/PALOMAR-2026-10-08-000007-v1/33131f4fb10067cb3009bf4db615d9680c1ccd6b",
        "source_repository": "leanprover-community/batteries"
      },
      {
        "commit": "10a2cfff285e1c7c2ebc49c0ba22cab0f3c58ee5",
        "fork_repository": "PalomarArchive/leanprover-community--import-graph--e0a79261b05a",
        "ref": "refs/tags/palomar/PALOMAR-2026-10-08-000007-v1/10a2cfff285e1c7c2ebc49c0ba22cab0f3c58ee5",
        "source_repository": "leanprover-community/import-graph"
      },
      {
        "commit": "29ff470276c725ae01505d55b17148c18fc7dfd3",
        "fork_repository": "PalomarArchive/leanprover-community--LeanSearchClient--9de355ab5f53",
        "ref": "refs/tags/palomar/PALOMAR-2026-10-08-000007-v1/29ff470276c725ae01505d55b17148c18fc7dfd3",
        "source_repository": "leanprover-community/LeanSearchClient"
      },
      {
        "commit": "a98628e16c11f5167f16124105ddce53efa9bfe5",
        "fork_repository": "PalomarArchive/leanprover-community--mathlib4--67b3d817d8a2",
        "ref": "refs/tags/palomar/PALOMAR-2026-10-08-000007-v1/a98628e16c11f5167f16124105ddce53efa9bfe5",
        "source_repository": "leanprover-community/mathlib4"
      },
      {
        "commit": "fb13df72ecefd8ddbf9291021d7f33a8673eb57b",
        "fork_repository": "PalomarArchive/leanprover-community--plausible--fb632f6f7bf4",
        "ref": "refs/tags/palomar/PALOMAR-2026-10-08-000007-v1/fb13df72ecefd8ddbf9291021d7f33a8673eb57b",
        "source_repository": "leanprover-community/plausible"
      },
      {
        "commit": "c643bbb3c24f8a25f9c14e3a6b1ceb13d01f3de1",
        "fork_repository": "PalomarArchive/leanprover-community--ProofWidgets4--26014acbbaff",
        "ref": "refs/tags/palomar/PALOMAR-2026-10-08-000007-v1/c643bbb3c24f8a25f9c14e3a6b1ceb13d01f3de1",
        "source_repository": "leanprover-community/ProofWidgets4"
      },
      {
        "commit": "37b0ba0b26109cf9f9c541f0f9557e50cfa1a3b9",
        "fork_repository": "PalomarArchive/leanprover-community--quote4--90d31d153685",
        "ref": "refs/tags/palomar/PALOMAR-2026-10-08-000007-v1/37b0ba0b26109cf9f9c541f0f9557e50cfa1a3b9",
        "source_repository": "leanprover-community/quote4"
      },
      {
        "commit": "843844fa601dd56767b1eb22b7ada5b64d5e567a",
        "fork_repository": "PalomarArchive/leanprover--lean4-cli--df175a7fc790",
        "ref": "refs/tags/palomar/PALOMAR-2026-10-08-000007-v1/843844fa601dd56767b1eb22b7ada5b64d5e567a",
        "source_repository": "leanprover/lean4-cli"
      }
    ]
  },
  "provenance": {
    "mathematical_sources": [
      {
        "authors": [],
        "location": "docs/ENDPOINT.md and docs/EXTENSIONS.md",
        "relationship": "formalizes",
        "title": "Sharp four-row permanent robustness, stability, and entropy",
        "type": "other"
      },
      {
        "authors": [
          {
            "name": "OpenAI"
          }
        ],
        "identifier": "https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-strict-four-row-permanent-inequality-and-permutation-moments-September-26-2026",
        "relationship": "adapts",
        "title": "A strict four-row permanent inequality and permutation moments",
        "type": "paper"
      },
      {
        "authors": [
          {
            "name": "Eric Carlen"
          },
          {
            "name": "Elliott H. Lieb"
          },
          {
            "name": "Michael Loss"
          }
        ],
        "identifier": "arXiv:math/0508096v1",
        "location": "https://arxiv.org/abs/math/0508096v1",
        "relationship": "background",
        "title": "An Inequality of Hadamard Type for Permanents",
        "type": "paper"
      },
      {
        "authors": [
          {
            "name": "Alexandre Bristiel"
          },
          {
            "name": "Pietro Caputo"
          }
        ],
        "identifier": "arXiv:2109.06009v3",
        "location": "https://arxiv.org/abs/2109.06009v3",
        "relationship": "background",
        "title": "Entropy inequalities for random walks and permutations",
        "type": "paper"
      },
      {
        "authors": [
          {
            "name": "Eric A. Carlen"
          },
          {
            "name": "Dario Cordero-Erausquin"
          }
        ],
        "identifier": "arXiv:0710.0870v2",
        "location": "https://arxiv.org/abs/0710.0870v2",
        "relationship": "background",
        "title": "Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities",
        "type": "paper"
      }
    ],
    "related_formalizations": [],
    "repository_role": "substantive-development",
    "responsible_maintainers": [
      {
        "name": "JD Jones"
      }
    ],
    "result_origin": "source-based"
  },
  "registered_at": "2026-10-08T20:26:30Z",
  "review": {
    "outcome": "neutral",
    "policy_commit": "96b034cc31a72a63d4f4041911dce337a85c9a04",
    "report": {
      "sha256": "bdcc7febdec7c2ddefa832b0e71e23929e67f112722039e41eb4903eb2644bca"
    },
    "reviewed_at": "2026-10-08T00:49:47Z",
    "reviewer_models": [
      "codex:gpt-6-sol"
    ],
    "warnings": []
  },
  "schema_version": 5,
  "source": {
    "commit": "861abe5342847d3f32985d55403547e1832ffac4",
    "license": {
      "declared_identifier": "MIT",
      "detected_identifier": "MIT",
      "path": "LICENSE",
      "sha256": "8d464f723696204001f7ef63b6146ffc544aa6837aa74c53f6f9c53d8a18b0f0"
    },
    "repository": "JD-Jones-ASES/four-row",
    "repository_url": "https://github.com/JD-Jones-ASES/four-row",
    "tree_url": "https://github.com/JD-Jones-ASES/four-row/tree/861abe5342847d3f32985d55403547e1832ffac4"
  },
  "status": "registered",
  "submission": {
    "authorization": {
      "relationship": "maintainer"
    },
    "submission_id": "990n09madwem"
  },
  "title": "Sharp robustness and stability of the four-row permanent inequality",
  "trust": {
    "challenge_bytes": 12398,
    "challenge_dependencies": [
      {
        "provenance": "allowlisted",
        "repository": "leanprover-community/mathlib4"
      }
    ],
    "challenge_imports": [
      "Mathlib.Analysis.SpecialFunctions.Pow.Real",
      "Mathlib.Data.EReal.Operations",
      "Mathlib.GroupTheory.Perm.Fin",
      "Mathlib.LinearAlgebra.Matrix.Permanent",
      "Mathlib.Tactic"
    ],
    "challenge_lines": 239,
    "level": "high",
    "reasons": []
  },
  "verification": {
    "bwrap_source_tag": "v0.12.0",
    "challenge_sha256": "944ee3cc29a54243d454deb01e4d688c35c069e689f8257f2d3dd49b9ba69af6",
    "evidence_path": "evidence/PALOMAR-2026-10-08-000007-v1/b675379100647419244e6c3879dfc59680d5f9938b79d02c4ebc16ffa6e37862/",
    "evidence_tree_sha256": "b675379100647419244e6c3879dfc59680d5f9938b79d02c4ebc16ffa6e37862",
    "kernels": [
      {
        "argv": [
          "/home/runner/.elan/toolchains/leanprover--lean4---v4.35.0-rc3/bin/nanoda_bin"
        ],
        "name": "nanoda"
      },
      {
        "argv": [
          "/home/runner/.elan/toolchains/leanprover--lean4---v4.35.0-rc3/bin/con-ron",
          "--jobs=2"
        ],
        "name": "con-ron"
      }
    ],
    "mechanical_report_sha256": "942da16bcc3f3931788fc3e24a51e1df7653f50770da155f9d509f676ca14494",
    "protected_config_sha256": "92e13d078b340feec3127d98995ae793c7522a303eddb8c27307fc4e70d008e1",
    "repository": "PalomarRegistry/PalomarSubmission",
    "run_id": 37651406740,
    "solution_sha256": "14c21e410a142b6d1f9e196c544cfa97b2dc733aa7e63f6bfbe41d9abb171c96",
    "tool_digests": {
      "bwrap": "07447ee0f1c1665d50b3ce4434d291f78a0f5213dad5cf13a02e3e119838fc24",
      "con-ron": "4e5616d94374cae37324dad2594f6230c2bb2297240249fc78ff508f3bc5acef",
      "lake": "8ba83c98f76562d03b8dbc33f1057151ba6cbb121679dde76b2260ccc90495e1",
      "lean": "bf8d54e4714cc4b03d3f6bb34c83b7202b87e49c8bfcbff6895c085bb90ceb38",
      "leanchecker": "9e36e955a251b1313c8eb5b7fa101282d51df109d34d8bb7c1cfdf51985aba29",
      "leanexport": "c5bc1a10a21e22cbb3671d65987cdef2076833b14182d823ccb2153adf2fa954",
      "nanoda_bin": "8241c5e6baa29490aa118d382f97961b208ae730fdb96545c2abed74c9ece5a8"
    },
    "toolchain_commit": "470d5ce1400764999581fd26d5d72b00d990b0f4",
    "verified_at": "2026-10-07T18:27:29Z",
    "workflow_commit": "d4e41c1d5b0d114c4859e6e5831dc6d3ad1d0d44",
    "workflow_path": ".github/workflows/submission.yml",
    "workflow_run_attempt": 1,
    "workflow_url": "https://github.com/PalomarRegistry/PalomarSubmission/actions/runs/37651406740"
  },
  "version": 1
}
