references/run_sabrina_entanglement_scattering_slack_identity.json

{
  "kernel": "run_sabrina_entanglement_scattering_slack_identity",
  "role": "post-computation assertion only",
  "schema": "ouroboros_scientific_reference_assertion_v1",
  "scientific_payload": {
    "claim_boundary": {
      "capabilities_removed": [],
      "flat_space_limit_extended": false,
      "general_configuration_reproved": false,
      "matter_entropy_terms_rederived": false,
      "quantum_task_dual_constructed": false,
      "source_error_claimed": false
    },
    "exact_checks": {
      "all_symbolic_residuals_zero": true,
      "archive_hash_matches": true,
      "entanglement_ridge_bound_present": true,
      "equality_iff_all_slacks_zero": true,
      "member_hash_matches": true,
      "mutual_information_equation_present": true,
      "mutual_information_ridge_bound_present": true,
      "numerical_witness_exact": true,
      "numerical_witness_geometric": true,
      "source_blocks_match": true,
      "two_focusing_equations_present": true
    },
    "paper": {
      "arxiv_id": "2604.22612",
      "title": "Generalized Entanglement Wedges and the Connected Wedge Theorem"
    },
    "result_version": "sabrina_entanglement_scattering_slack_identity_v1",
    "source_evidence": {
      "archive_sha256": "8a55509c4b902e68016cb16a722efeb692056e6530cb2d6838b87fe77d6d84f6",
      "block_hashes": {
        "future_work_scope": "53879de714d7277342abc026d9e3697f1d6779fa225bcb29545c76cbc6b177f4",
        "mutual_information_definition": "180f95e32264465f0b06a545094bbc73fe1b5a07fc6e5b02e2dce4ec06bec1a1",
        "warmup_entanglement_ridge": "ba55cae873427b912363ea39970fb97d305e2e96912512479cbd6dfe54cf36ba",
        "warmup_mutual_information_ridge": "2c8e40f06fdad817d5882b4e71e7ab6cc8d678c36ec327735d5c729b84d9047a"
      },
      "checks": {
        "archive_hash_matches": true,
        "entanglement_ridge_bound_present": true,
        "member_hash_matches": true,
        "mutual_information_equation_present": true,
        "mutual_information_ridge_bound_present": true,
        "source_blocks_match": true,
        "two_focusing_equations_present": true
      },
      "member_sha256": "67a3bec7a35d950e982ea7edeccca1c7f0401539106bd1edbfea9e3b80013b0e"
    },
    "status": "complete",
    "symbolic_certificate": {
      "definitions": {
        "delta_min": "Area(D) - [Area(E(V_1)) + Area(E(V_2))]",
        "sigma_ent": "4 G_N S_gen(s_ent) - 2 Area(R_ent)",
        "sigma_lift": "-[Area(D) - Area(A) - 2 Area(R_ent)]",
        "sigma_slope": "Area(E(X_1 union X_2)) - Area(A)"
      },
      "equality_grid": [
        {
          "all_slacks_zero": true,
          "gap_zero": true,
          "mask": 0,
          "numerator": "0"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 1,
          "numerator": "1"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 2,
          "numerator": "1"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 3,
          "numerator": "2"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 4,
          "numerator": "1"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 5,
          "numerator": "2"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 6,
          "numerator": "2"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 7,
          "numerator": "3"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 8,
          "numerator": "1"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 9,
          "numerator": "2"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 10,
          "numerator": "2"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 11,
          "numerator": "3"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 12,
          "numerator": "2"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 13,
          "numerator": "3"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 14,
          "numerator": "3"
        },
        {
          "all_slacks_zero": false,
          "gap_zero": false,
          "mask": 15,
          "numerator": "4"
        }
      ],
      "gap": "(delta_min + sigma_ent + sigma_lift + sigma_slope)/(4*G_N)",
      "gap_numerator": "delta_min + sigma_ent + sigma_lift + sigma_slope",
      "numerical_witness": {
        "all_primitive_areas_positive": true,
        "expected_gap": "51/28",
        "gap": "51/28"
      },
      "residuals": {
        "entanglement_focusing": "0",
        "gap_identity": "0",
        "lift_focusing": "0",
        "minimality": "0",
        "slope_focusing": "0"
      }
    },
    "theorem": {
      "identity": "S_gen(s_ent)-I(V_1;V_2)=(sigma_ent+delta_min+sigma_lift+sigma_slope)/(4 G_N)",
      "positivity": "all four slacks are nonnegative when G_N>0",
      "regime": "the paper's warm-up entanglement-scattering configuration and its stated focusing/minimality assumptions",
      "saturation": "equality holds if and only if all four slacks vanish"
    }
  },
  "scientific_payload_sha256": "65ed4ac892b7bc06c0e00a75b8253eceebe84a4342dbbdfc165c226b7a62fdf3"
}