{
  "checker_repository": "https://github.com/Mikael-Codes/hegelese",
  "checker_commit": "3199a7fd4d83ab061c5d445d28be6c07edb0d61e",
  "checker_sha256": "f64de70ed86c4988871ed3d66ee1241ff97a40e4c95816217526444ec49215c9",
  "checker_version": "0.3.0",
  "python_version": "3.14.7",
  "algebra": {
    "field": "F2",
    "labels": 4,
    "non_root_labels": [
      1,
      2,
      3
    ],
    "basis_subset_masks": [
      1,
      2,
      3,
      4,
      5,
      6,
      7
    ],
    "source_dimension": 7,
    "state_encoding": "bit i is the coefficient of t_A for A with mask i+1"
  },
  "cases": [
    {
      "case": "identity",
      "source_states": 128,
      "target_states": 128,
      "status": "ExhaustivelyChecked",
      "accepted": true,
      "checks_completed": 1281,
      "failures": 0,
      "erased_pairs": 0,
      "retained_coordinate_masks": [
        1,
        2,
        3,
        4,
        5,
        6,
        7
      ]
    },
    {
      "case": "quotient_J3",
      "source_states": 128,
      "target_states": 64,
      "status": "ExhaustivelyChecked",
      "accepted": true,
      "checks_completed": 1281,
      "failures": 0,
      "erased_pairs": 64,
      "retained_coordinate_masks": [
        1,
        2,
        3,
        4,
        5,
        6
      ]
    },
    {
      "case": "quotient_J2",
      "source_states": 128,
      "target_states": 8,
      "status": "ExhaustivelyChecked",
      "accepted": true,
      "checks_completed": 1281,
      "failures": 0,
      "erased_pairs": 960,
      "retained_coordinate_masks": [
        1,
        2,
        4
      ]
    },
    {
      "case": "negative_exactState",
      "source_states": 128,
      "target_states": 8,
      "status": "Refuted",
      "accepted": false,
      "checks_completed": 1409,
      "failures": 120,
      "erased_pairs": 960,
      "retained_coordinate_masks": [
        1,
        2,
        4
      ]
    }
  ],
  "checked_scope": "One finite object, all 128 vector states, all 7 addition inputs, declared retained observations.",
  "not_checked": [
    "Naturality over maps of finite label sets",
    "Reconstruction from objects of size at most r",
    "Universal factorization or optimality",
    "Lineage acceptance"
  ],
  "theorem_interpretation": {
    "source": "Binary-cut reconstruction preprint v2",
    "status": "External mathematical interpretation, not a Hegelese checker verdict",
    "claim": "For natural linear quotients of J with ordinary reconstruction cutoff r=3, J/J^2 is the universal most informative admissible quotient; identity J and J/J^3 do not meet that global cutoff."
  },
  "separate_reconstruction_check": {
    "method": "Exact GF2 comparison matrix into the kernel of the normalized Roos differential",
    "checker_sha256": "e072aa39bca31a86548776fea1960c2567aa873a7d9bbd9c84ecb0844864a11b",
    "cases": [
      {
        "case": "identity",
        "n": 4,
        "r": 3,
        "augmentation_cutoff_d": null,
        "source_dimension": 7,
        "limit_dimension": 7,
        "comparison_rank": 6,
        "kernel_dimension": 1,
        "cokernel_dimension": 1,
        "H1_dimension": 1,
        "cochain_dimensions": [
          18,
          12
        ],
        "differential_ranks": [
          11
        ],
        "ordinary_comparison_is_isomorphism": false
      },
      {
        "case": "quotient_J3",
        "n": 4,
        "r": 3,
        "augmentation_cutoff_d": 3,
        "source_dimension": 6,
        "limit_dimension": 7,
        "comparison_rank": 6,
        "kernel_dimension": 0,
        "cokernel_dimension": 1,
        "H1_dimension": 1,
        "cochain_dimensions": [
          18,
          12
        ],
        "differential_ranks": [
          11
        ],
        "ordinary_comparison_is_isomorphism": false
      },
      {
        "case": "quotient_J2",
        "n": 4,
        "r": 3,
        "augmentation_cutoff_d": 2,
        "source_dimension": 3,
        "limit_dimension": 3,
        "comparison_rank": 3,
        "kernel_dimension": 0,
        "cokernel_dimension": 0,
        "H1_dimension": 1,
        "cochain_dimensions": [
          14,
          12
        ],
        "differential_ranks": [
          11
        ],
        "ordinary_comparison_is_isomorphism": true
      }
    ],
    "scope": "One four-label reconstruction diagram. This finite calculation is not a proof of the universal theorem."
  }
}