{
  "submission": "submission/zcy_10_30/P95_n1_n7_real_optima_20261029T1836.zip",
  "verdict": "PASS: continuous arbitrary-angle global optimality n=1..7; newly proved on site n=5..7",
  "bundled_replay": {
    "passed": true,
    "manifest_files_verified": 22,
    "optimum_sides": {
      "1": "2",
      "2": "4",
      "3": "6",
      "4": "8",
      "5": "11",
      "6": "14",
      "7": "17"
    },
    "scope": "Arbitrary real angles and real square side; boundary touching allowed.",
    "lower_bound_n1_n4": "Analytic largest-domino projection proof in DERIVATION_ZH.md section 2; not a discrete grid argument.",
    "trust_boundary": "Human-reviewed analytic arguments plus independently implemented rational replay, not formal proof-assistant verification.",
    "witnesses": [
      {
        "valid": true,
        "method": "exact rational vertices and separating axis theorem; no tolerance",
        "n": 1,
        "side": "2",
        "rectangle_area": 2,
        "unused_area_exact": "2",
        "pairs_checked": 0,
        "nonzero_turns": 0,
        "all_vertices_in_square": true,
        "all_interiors_disjoint": true,
        "schema_and_decimal_strings_valid": true,
        "expected_n": 1,
        "sha256": "5fe1c46dee96d343e712ed0fa8155b79abc60c9251669766ed4905303d1e4cd1"
      },
      {
        "valid": true,
        "method": "exact rational vertices and separating axis theorem; no tolerance",
        "n": 2,
        "side": "4",
        "rectangle_area": 10,
        "unused_area_exact": "6",
        "pairs_checked": 1,
        "nonzero_turns": 0,
        "all_vertices_in_square": true,
        "all_interiors_disjoint": true,
        "schema_and_decimal_strings_valid": true,
        "expected_n": 2,
        "sha256": "26c213e01601ad540225d41ae43f4afdce3760040785c8fedd95b6a654745b5d"
      },
      {
        "valid": true,
        "method": "exact rational vertices and separating axis theorem; no tolerance",
        "n": 3,
        "side": "6",
        "rectangle_area": 28,
        "unused_area_exact": "8",
        "pairs_checked": 3,
        "nonzero_turns": 0,
        "all_vertices_in_square": true,
        "all_interiors_disjoint": true,
        "schema_and_decimal_strings_valid": true,
        "expected_n": 3,
        "sha256": "a7b36ae14b03756a19c032815f983fd91ea4be1016d750bb8ad361c60b192901"
      },
      {
        "valid": true,
        "method": "exact rational vertices and separating axis theorem; no tolerance",
        "n": 4,
        "side": "8",
        "rectangle_area": 60,
        "unused_area_exact": "4",
        "pairs_checked": 6,
        "nonzero_turns": 0,
        "all_vertices_in_square": true,
        "all_interiors_disjoint": true,
        "schema_and_decimal_strings_valid": true,
        "expected_n": 4,
        "sha256": "9171d383be953f3b6f1dbac5cfb55f05af18683dcd6b4506af15bb6285a50ab0"
      },
      {
        "valid": true,
        "method": "exact rational vertices and separating axis theorem; no tolerance",
        "n": 5,
        "side": "11",
        "rectangle_area": 110,
        "unused_area_exact": "11",
        "pairs_checked": 10,
        "nonzero_turns": 0,
        "all_vertices_in_square": true,
        "all_interiors_disjoint": true,
        "schema_and_decimal_strings_valid": true,
        "expected_n": 5,
        "sha256": "c56a2a799a442d6cc63c0e42192c09e76a853aaabc493ed783bd12bff7118fdb"
      },
      {
        "valid": true,
        "method": "exact rational vertices and separating axis theorem; no tolerance",
        "n": 6,
        "side": "14",
        "rectangle_area": 182,
        "unused_area_exact": "14",
        "pairs_checked": 15,
        "nonzero_turns": 0,
        "all_vertices_in_square": true,
        "all_interiors_disjoint": true,
        "schema_and_decimal_strings_valid": true,
        "expected_n": 6,
        "sha256": "1adf6e450c587763ab526606ccfbdca875867fa56adbc2f31c5629b2fc50b6fe"
      },
      {
        "valid": true,
        "method": "exact rational vertices and separating axis theorem; no tolerance",
        "n": 7,
        "side": "17",
        "rectangle_area": 280,
        "unused_area_exact": "9",
        "pairs_checked": 21,
        "nonzero_turns": 0,
        "all_vertices_in_square": true,
        "all_interiors_disjoint": true,
        "schema_and_decimal_strings_valid": true,
        "expected_n": 7,
        "sha256": "b557e2386204322b2cf66c8eb96f5805b1c20c62d09b2857fb0e4214f58caa68"
      }
    ],
    "strict_target_trees": [
      {
        "complete_tree_verified": true,
        "independent_geometry": true,
        "pieces": [
          3,
          4,
          5
        ],
        "target": "11",
        "nodes_checked": 1409,
        "duals_checked": 11184,
        "pair_branch_prunes": 14287,
        "wall_leaves": 12,
        "analytic_pair35_leaves": 16,
        "pending_stack": 0,
        "exclusion_comparison": "strict_less_than",
        "analytic_lemma_sha256": "4db4c52bfd242d240019e42122d4c94c504f35b9fc5cac1a6fb8dd176d25dd63",
        "certificate_sha256": "4f2cdb350ae4f8e68e0cbece2720d0c396118306a7916d14dfe6794d54dec3da",
        "checker_sha256": "2b6d63f5c20ed83f75ea0a5f7e3b65a452e72e1325fe219003a783e1274ecd15",
        "seconds": 2.0,
        "proof_scope": "Only complete_tree_verified=true excludes all continuously rotating packings of the stated subset with side STRICTLY LESS than target11. Equality11 is allowed. A separately exact-validated side11 complete witness then establishes the real-valued global optimum."
      },
      {
        "complete_tree_verified": true,
        "independent_geometry": true,
        "pieces": [
          4,
          5,
          6
        ],
        "target": "14",
        "nodes_checked": 1927,
        "duals_checked": 16068,
        "pair_branch_prunes": 15306,
        "wall_leaves": 0,
        "analytic_consecutive_pair_leaves": 16,
        "pending_stack": 0,
        "exclusion_comparison": "strict_less_than",
        "analytic_lemma_sha256": "d583763849865a121d9fcc125f2731b6f90609c574b31f351672879c2a6a9a41",
        "certificate_sha256": "47d1ddda82e92de5205acc6ffee00f0f532434db1829c23b54983c77321d0bd1",
        "checker_sha256": "e1cdf211ab76508a5293473599cb886c85e8f8a30e356f4dff7b6291ff135a64",
        "seconds": 3.25,
        "proof_scope": "Only complete_tree_verified=true excludes all continuously rotating packings of the stated subset with side STRICTLY LESS than the stated target. Equality is allowed. A separately exact-validated complete full-n witness at the target then establishes its real-valued global optimum."
      },
      {
        "complete_tree_verified": true,
        "independent_geometry": true,
        "pieces": [
          5,
          6,
          7
        ],
        "target": "17",
        "nodes_checked": 2431,
        "duals_checked": 20118,
        "pair_branch_prunes": 16276,
        "wall_leaves": 0,
        "analytic_consecutive_pair_leaves": 19,
        "pending_stack": 0,
        "exclusion_comparison": "strict_less_than",
        "analytic_lemma_sha256": "d583763849865a121d9fcc125f2731b6f90609c574b31f351672879c2a6a9a41",
        "certificate_sha256": "dafcd893b27d74b43ae2b555eaccc5b3af35ec7b4bf232e84aa5a28b1fa6c00d",
        "checker_sha256": "e1cdf211ab76508a5293473599cb886c85e8f8a30e356f4dff7b6291ff135a64",
        "seconds": 4.531000000075437,
        "proof_scope": "Only complete_tree_verified=true excludes all continuously rotating packings of the stated subset with side STRICTLY LESS than the stated target. Equality is allowed. A separately exact-validated complete full-n witness at the target then establishes its real-valued global optimum."
      }
    ]
  },
  "independent_replay": {
    "archive_sha256": "25237c2a5a8ec4754d4c63c81a178abed4c839363db819dd96db9eac443757bd",
    "trees": [
      {
        "n": 5,
        "target": 11,
        "nodes": 1409,
        "duals": 11184,
        "analytic": 16,
        "walls": 12,
        "pair_prunes": 14287
      },
      {
        "n": 6,
        "target": 14,
        "nodes": 1927,
        "duals": 16068,
        "analytic": 16,
        "walls": 0,
        "pair_prunes": 15306
      },
      {
        "n": 7,
        "target": 17,
        "nodes": 2431,
        "duals": 20118,
        "analytic": 19,
        "walls": 0,
        "pair_prunes": 16276
      }
    ],
    "negative_controls": [
      {
        "case": "missing_final_node",
        "rejected": true,
        "reason": "incomplete tree"
      },
      {
        "case": "duplicate_node",
        "rejected": true,
        "reason": "node/inheritance"
      },
      {
        "case": "zero_dual",
        "rejected": true,
        "reason": "dual contradiction"
      },
      {
        "case": "analytic_leaf_outside_cone",
        "rejected": true,
        "reason": "analytic domain"
      }
    ],
    "passed": true,
    "seconds": 14.14000000001397,
    "trust_boundary": "Manually reviewed near-axis lemma and SAT; exact certificate replay, not proof-assistant formalization."
  },
  "site_verifier_witnesses": [
    {
      "n": 1,
      "valid": true,
      "score": "2000000000",
      "displayScore": "2",
      "message": "答案有效，验证器已接受这份答案。",
      "messageEn": "The answer is valid; the verifier accepted it."
    },
    {
      "n": 2,
      "valid": true,
      "score": "4000000000",
      "displayScore": "4",
      "message": "答案有效，验证器已接受这份答案。",
      "messageEn": "The answer is valid; the verifier accepted it."
    },
    {
      "n": 3,
      "valid": true,
      "score": "6000000000",
      "displayScore": "6",
      "message": "答案有效，验证器已接受这份答案。",
      "messageEn": "The answer is valid; the verifier accepted it."
    },
    {
      "n": 4,
      "valid": true,
      "score": "8000000000",
      "displayScore": "8",
      "message": "答案有效，验证器已接受这份答案。",
      "messageEn": "The answer is valid; the verifier accepted it."
    },
    {
      "n": 5,
      "valid": true,
      "score": "11000000000",
      "displayScore": "11",
      "message": "答案有效，验证器已接受这份答案。",
      "messageEn": "The answer is valid; the verifier accepted it."
    },
    {
      "n": 6,
      "valid": true,
      "score": "14000000000",
      "displayScore": "14",
      "message": "答案有效，验证器已接受这份答案。",
      "messageEn": "The answer is valid; the verifier accepted it."
    },
    {
      "n": 7,
      "valid": true,
      "score": "17000000000",
      "displayScore": "17",
      "message": "答案有效，验证器已接受这份答案。",
      "messageEn": "The answer is valid; the verifier accepted it."
    }
  ],
  "independent_checker_sha256": "1e5e7fb4ee1bb43caeea02dec39c67c5158b3e9fde55f4b745bf117f9d5f04da"
}