{
  "kernel": "run_sabrina_points_scattering_lower_slack_identity",
  "role": "post-computation assertion only",
  "schema": "ouroboros_scientific_reference_assertion_v1",
  "scientific_payload": {
    "claim_boundary": {
      "capabilities_removed": [],
      "new_dynamical_equivalence_claimed": false,
      "semiclassical_entropy_inequalities_only": true
    },
    "exact_checks": {
      "all_chain_residuals_zero": true,
      "all_sixteen_masks_checked": true,
      "all_slacks_nonnegative": true,
      "archive_hash_matches": true,
      "cwt_ridge_bound_present": true,
      "final_lower_chain_present": true,
      "gap_is_exact_slack_sum": true,
      "max_wedge_bound_present": true,
      "member_hash_matches": true,
      "points_focus_bound_present": true,
      "ridge_order_present": true,
      "saturation_iff_all_slacks_zero": true,
      "source_blocks_match": true,
      "unique_binary_saturation_mask": true
    },
    "paper": {
      "arxiv_id": "2604.22612",
      "title": "Generalized Entanglement Wedges and the Connected Wedge Theorem"
    },
    "result_version": "sabrina_points_scattering_lower_slack_identity_v1",
    "source_evidence": {
      "archive_sha256": "8a55509c4b902e68016cb16a722efeb692056e6530cb2d6838b87fe77d6d84f6",
      "block_hashes": {
        "cwt_ridge_bound": "53d435b08fb84b5368ad548c6a03644afd5a9e8bf7e040d7d25d1bb83d1ccba5",
        "max_wedge_entropy_bound": "83e0923ad85ce26ff185b4eb4ca49f7c292dd40adda74bc8cacd7800e4ea4bc5",
        "points_lower_bound_chain": "647182fc3b6ffc3b9af688727b199766ce64c44b9573f4ce8798f2f0d5974689"
      },
      "checks": {
        "archive_hash_matches": true,
        "cwt_ridge_bound_present": true,
        "final_lower_chain_present": true,
        "max_wedge_bound_present": true,
        "member_hash_matches": true,
        "points_focus_bound_present": true,
        "ridge_order_present": true,
        "source_blocks_match": true
      },
      "member_sha256": "67a3bec7a35d950e982ea7edeccca1c7f0401539106bd1edbfea9e3b80013b0e"
    },
    "status": "complete",
    "symbolic_certificate": {
      "checks": {
        "all_chain_residuals_zero": true,
        "all_sixteen_masks_checked": true,
        "all_slacks_nonnegative": true,
        "gap_is_exact_slack_sum": true,
        "saturation_iff_all_slacks_zero": true,
        "unique_binary_saturation_mask": true
      },
      "equality_rows": [
        {
          "all_slacks_zero": true,
          "gap": "0",
          "gap_zero": true,
          "mask": 0
        },
        {
          "all_slacks_zero": false,
          "gap": "1",
          "gap_zero": false,
          "mask": 1
        },
        {
          "all_slacks_zero": false,
          "gap": "1",
          "gap_zero": false,
          "mask": 2
        },
        {
          "all_slacks_zero": false,
          "gap": "2",
          "gap_zero": false,
          "mask": 3
        },
        {
          "all_slacks_zero": false,
          "gap": "1",
          "gap_zero": false,
          "mask": 4
        },
        {
          "all_slacks_zero": false,
          "gap": "2",
          "gap_zero": false,
          "mask": 5
        },
        {
          "all_slacks_zero": false,
          "gap": "2",
          "gap_zero": false,
          "mask": 6
        },
        {
          "all_slacks_zero": false,
          "gap": "3",
          "gap_zero": false,
          "mask": 7
        },
        {
          "all_slacks_zero": false,
          "gap": "1",
          "gap_zero": false,
          "mask": 8
        },
        {
          "all_slacks_zero": false,
          "gap": "2",
          "gap_zero": false,
          "mask": 9
        },
        {
          "all_slacks_zero": false,
          "gap": "2",
          "gap_zero": false,
          "mask": 10
        },
        {
          "all_slacks_zero": false,
          "gap": "3",
          "gap_zero": false,
          "mask": 11
        },
        {
          "all_slacks_zero": false,
          "gap": "2",
          "gap_zero": false,
          "mask": 12
        },
        {
          "all_slacks_zero": false,
          "gap": "3",
          "gap_zero": false,
          "mask": 13
        },
        {
          "all_slacks_zero": false,
          "gap": "3",
          "gap_zero": false,
          "mask": 14
        },
        {
          "all_slacks_zero": false,
          "gap": "4",
          "gap_zero": false,
          "mask": 15
        }
      ],
      "gap_identity": "I(V1;V2)-S_gen(e_max(s_pts''))=delta_CWT+delta_ridge+delta_focus+delta_max",
      "residuals": {
        "cwt_step": "0",
        "focus_step": "0",
        "gap_identity": "0",
        "max_wedge_step": "0",
        "ridge_step": "0"
      },
      "symbolic_gap": "delta_CWT + delta_focus + delta_max + delta_ridge"
    },
    "theorem": {
      "lower_gap_identity": "I(V1;V2)-S_gen(e_max(s_pts''))=delta_CWT+delta_ridge+delta_focus+delta_max",
      "saturation": "the lower bound saturates if and only if all four source inequalities saturate simultaneously",
      "slack_meanings": {
        "delta_CWT": "I(V1;V2)-Area(R_reg)/(2G_N)",
        "delta_focus": "Area(R_pts)/(2G_N)-S_gen(s_pts'')",
        "delta_max": "S_gen(s_pts'')-S_gen(e_max(s_pts''))",
        "delta_ridge": "[Area(R_reg)-Area(R_pts)]/(2G_N)"
      }
    }
  },
  "scientific_payload_sha256": "7f9b013510e795182939e14d751abafa52301bf7e7cd140ff4fa5a32a2b8db69"
}