{
  "kernel": "run_sabrina_low_hard_generator_nonclosure",
  "role": "post-computation assertion only",
  "schema": "ouroboros_scientific_reference_assertion_v1",
  "scientific_payload": {
    "claim_boundary": {
      "capabilities_removed": [],
      "full_soft_plus_hard_algebra_failure_claimed": false,
      "hard_scalar_truncation_only": true,
      "massless_qed_context_only": true
    },
    "commutator_certificate": {
      "angular_component": "0",
      "checks": {
        "angular_component_zero": true,
        "connection_derivative_cancels": true,
        "energy_component_exact": true,
        "same_family_requires_zero_label": true,
        "zero_obstruction_gives_zero_commutator": true
      },
      "energy_component": "-(Gamma*Y*Z_1 - Gamma*Y_1*Z + Y*Z_2 - Y_2*Z)/E",
      "expected_energy_component": "(-Gamma*(Y*Z_1 - Y_1*Z) - Y*Z_2 + Y_2*Z)/E"
    },
    "exact_checks": {
      "all_forty_nine_pairs_checked": true,
      "all_mode_formulas_exact": true,
      "angular_component_zero": true,
      "archive_hash_matches": true,
      "connection_derivative_cancels": true,
      "decompressed_member_hash_matches": true,
      "energy_component_exact": true,
      "explicit_m1_n2_witness": true,
      "generic_nonclosure_count": true,
      "incoming_hard_charge_present": true,
      "outgoing_hard_charge_present": true,
      "same_family_requires_zero_label": true,
      "scalar_hard_operator_present": true,
      "soft_plus_hard_completion_present": true,
      "source_blocks_match": true,
      "ward_identity_present": true,
      "zero_locus_exact": true,
      "zero_obstruction_gives_zero_commutator": true
    },
    "monomial_certificate": {
      "checks": {
        "all_forty_nine_pairs_checked": true,
        "all_mode_formulas_exact": true,
        "explicit_m1_n2_witness": true,
        "generic_nonclosure_count": true,
        "zero_locus_exact": true
      },
      "rows": [
        {
          "coefficient": "0",
          "commutator_zero": true,
          "formula_exact": true,
          "m": 0,
          "n": 0
        },
        {
          "coefficient": "0",
          "commutator_zero": true,
          "formula_exact": true,
          "m": 0,
          "n": 1
        },
        {
          "coefficient": "-2",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 0,
          "n": 2
        },
        {
          "coefficient": "-6*z",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 0,
          "n": 3
        },
        {
          "coefficient": "-12*z**2",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 0,
          "n": 4
        },
        {
          "coefficient": "-20*z**3",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 0,
          "n": 5
        },
        {
          "coefficient": "-30*z**4",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 0,
          "n": 6
        },
        {
          "coefficient": "0",
          "commutator_zero": true,
          "formula_exact": true,
          "m": 1,
          "n": 0
        },
        {
          "coefficient": "0",
          "commutator_zero": true,
          "formula_exact": true,
          "m": 1,
          "n": 1
        },
        {
          "coefficient": "-2*z",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 1,
          "n": 2
        },
        {
          "coefficient": "-6*z**2",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 1,
          "n": 3
        },
        {
          "coefficient": "-12*z**3",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 1,
          "n": 4
        },
        {
          "coefficient": "-20*z**4",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 1,
          "n": 5
        },
        {
          "coefficient": "-30*z**5",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 1,
          "n": 6
        },
        {
          "coefficient": "2",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 2,
          "n": 0
        },
        {
          "coefficient": "2*z",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 2,
          "n": 1
        },
        {
          "coefficient": "0",
          "commutator_zero": true,
          "formula_exact": true,
          "m": 2,
          "n": 2
        },
        {
          "coefficient": "-4*z**3",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 2,
          "n": 3
        },
        {
          "coefficient": "-10*z**4",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 2,
          "n": 4
        },
        {
          "coefficient": "-18*z**5",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 2,
          "n": 5
        },
        {
          "coefficient": "-28*z**6",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 2,
          "n": 6
        },
        {
          "coefficient": "6*z",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 3,
          "n": 0
        },
        {
          "coefficient": "6*z**2",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 3,
          "n": 1
        },
        {
          "coefficient": "4*z**3",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 3,
          "n": 2
        },
        {
          "coefficient": "0",
          "commutator_zero": true,
          "formula_exact": true,
          "m": 3,
          "n": 3
        },
        {
          "coefficient": "-6*z**5",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 3,
          "n": 4
        },
        {
          "coefficient": "-14*z**6",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 3,
          "n": 5
        },
        {
          "coefficient": "-24*z**7",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 3,
          "n": 6
        },
        {
          "coefficient": "12*z**2",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 4,
          "n": 0
        },
        {
          "coefficient": "12*z**3",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 4,
          "n": 1
        },
        {
          "coefficient": "10*z**4",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 4,
          "n": 2
        },
        {
          "coefficient": "6*z**5",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 4,
          "n": 3
        },
        {
          "coefficient": "0",
          "commutator_zero": true,
          "formula_exact": true,
          "m": 4,
          "n": 4
        },
        {
          "coefficient": "-8*z**7",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 4,
          "n": 5
        },
        {
          "coefficient": "-18*z**8",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 4,
          "n": 6
        },
        {
          "coefficient": "20*z**3",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 5,
          "n": 0
        },
        {
          "coefficient": "20*z**4",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 5,
          "n": 1
        },
        {
          "coefficient": "18*z**5",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 5,
          "n": 2
        },
        {
          "coefficient": "14*z**6",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 5,
          "n": 3
        },
        {
          "coefficient": "8*z**7",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 5,
          "n": 4
        },
        {
          "coefficient": "0",
          "commutator_zero": true,
          "formula_exact": true,
          "m": 5,
          "n": 5
        },
        {
          "coefficient": "-10*z**9",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 5,
          "n": 6
        },
        {
          "coefficient": "30*z**4",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 6,
          "n": 0
        },
        {
          "coefficient": "30*z**5",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 6,
          "n": 1
        },
        {
          "coefficient": "28*z**6",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 6,
          "n": 2
        },
        {
          "coefficient": "24*z**7",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 6,
          "n": 3
        },
        {
          "coefficient": "18*z**8",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 6,
          "n": 4
        },
        {
          "coefficient": "10*z**9",
          "commutator_zero": false,
          "formula_exact": true,
          "m": 6,
          "n": 5
        },
        {
          "coefficient": "0",
          "commutator_zero": true,
          "formula_exact": true,
          "m": 6,
          "n": 6
        }
      ],
      "zero_pairs": [
        [
          0,
          0
        ],
        [
          0,
          1
        ],
        [
          1,
          0
        ],
        [
          1,
          1
        ],
        [
          2,
          2
        ],
        [
          3,
          3
        ],
        [
          4,
          4
        ],
        [
          5,
          5
        ],
        [
          6,
          6
        ]
      ]
    },
    "paper": {
      "arxiv_id": "1407.3814",
      "title": "Low's Subleading Soft Theorem as a Symmetry of QED"
    },
    "result_version": "sabrina_low_hard_generator_nonclosure_v1",
    "source_evidence": {
      "archive_sha256": "56dd48c217761e4cfc914fc3480831c01049a5e34b6ed4ef11893fc445964043",
      "block_hashes": {
        "soft_to_symmetry_hard_generator": "a85fe5207d3e2b66985bb44637b1ec1e6a838b5729964b31b85ec5f077e3430c"
      },
      "checks": {
        "archive_hash_matches": true,
        "decompressed_member_hash_matches": true,
        "incoming_hard_charge_present": true,
        "outgoing_hard_charge_present": true,
        "scalar_hard_operator_present": true,
        "soft_plus_hard_completion_present": true,
        "source_blocks_match": true,
        "ward_identity_present": true
      },
      "member_sha256": "b136e79a81fe707dac8d99c8bc5e9c72fe7162ba771dd2887cd878305aadce66"
    },
    "status": "complete",
    "theorem": {
      "angular_component": "zero",
      "closure_obstruction": "the commutator is in the same X_U family only when the displayed covariant derivative vanishes",
      "commutator": "[X_Y,X_Z]=-E^-1 D_z(Y partial_z Z-Z partial_z Y) partial_E",
      "monomial_modes": "for Y=z^m,Z=z^n and Gamma=0, the coefficient is -(n-m)(m+n-1)z^(m+n-2)/E"
    }
  },
  "scientific_payload_sha256": "923662d26ef1703e8e9b20da3584065e853328708a7abc6c4e522e16abb2d9b5"
}