{
  "schema": "csl.hull-benchmark-records/1",
  "report_id": "opt06-basis-reuse-20261014-ef70e8c5-r2",
  "created_utc": "2026-10-14T01:08:34Z",
  "code_commit": "ef70e8c580a9556b0f5d96e49070d33221bf5b64",
  "source_worktree_head": "ef70e8c580a9556b0f5d96e49070d33221bf5b64",
  "algorithm": {
    "name": "within-solve phase-I basis-reuse hull classification",
    "implementation": "CSL::geometry::reduce_hull_basis_reuse",
    "source": "src/geometry/basis_reuse_reducer.cpp"
  },
  "backend": {
    "name": "HiGHS LP adapter",
    "version": "1.11.0",
    "configured_threads": 1,
    "presolve": "off",
    "parallel": "off"
  },
  "counter_semantics": {
    "lp_calls": "caller-workspace membership/candidate LP calls; excludes phase-I basis solve",
    "basis_solves": "dedicated within-solve phase-I LP solves for basis classification"
  },
  "complexity": {
    "representation": "For n points in R^d, the Phase-I formulation has n structural variables and d+1 equalities. The assembled matrix stores (d+1)n coefficients, O(nd), plus O(n+d) indexing/RHS data; solver workspace/factorization storage is backend dependent.",
    "work": "One Phase-I LP solve is performed. At most n basis-coordinate queries and exact convex-combination certification attempts are made (one per nonbasis candidate; actual count depends on basis and validation outcomes). Each certificate uses at most d+1 structural basis points. The Phase-I LP solve cost is backend dependent; no general runtime bound or scaling claim is stated."
  },
  "evaluation_plan": "This report tests small permuted, duplicate/degenerate, and interior-basis 2D clouds against the generic LP-membership reducer. Follow-up evaluation should vary n and d, rank/degeneracy, duplicates and interior/face points, compare paired outputs to the same baseline, retain exact counter and failure records, and use a separate limiter profile before any performance conclusion. Include fuel-consumption workloads when the matching scenario fixture is available.",
  "build": {
    "source_code_commit": "ef70e8c580a9556b0f5d96e49070d33221bf5b64",
    "source_identity_scope": "tracked algorithm sources at code_commit; measurement harness is separately hashed",
    "build_generator": "Visual Studio 17 2022",
    "build_platform": "x64",
    "configuration": "Release",
    "compiler": "MSVC cl.exe (Hostx64/x64)",
    "compiler_id": "MSVC",
    "compiler_version": "19.44.35215.0",
    "release_flags": "/O2 /Ob2 /DNDEBUG",
    "cxx_standard": "20",
    "configured_dependency_highs": "1.11.0",
    "executable_sha256": "5f3107b3fa707cfcdecc38ec178ad3644ed430fb74ab6e7694ec10fdafc23dcf",
    "build_log_sha256": "c585ec5b9b1de7d7479990781d8fac64ee9e9373544921ef8fd679fa133c5082",
    "cmake_cache_sha256": "70630b1fa9237d77f77616fbd885edd524d2bb4ac7b500902c1f19ce6829b11d",
    "algorithm_source_sha256": {
      "src/geometry/basis_reuse_reducer.cpp": "71ae697f0beea2338792573213f56d475cb251b4d4ba87d17212c92a873e8e08",
      "src/geometry/hull_reducer.cpp": "a0dab69a6e598f4f9c49108b8c54315dbdeed488082ae791fda22521961d8161",
      "include/csl/geometry/basis_reuse_reducer.hpp": "f4c3d05c7fc31dc655f37231e0eeef970e96f569d2652fa643315e537e0eb1ce",
      "include/csl/geometry/hull_reducer.hpp": "4d7a96872d01bbbb12989b28323b5868908ca6c4582635a89a871b56ac321e5c"
    },
    "harness_sha256": "2ef0f5b66be32bdda930dc2033a9bb2e434fd5b77446e8e29e93311278abdb17",
    "build_command": "cmake --build opt06-report-build-v2 --config Release --target csl_opt06_measure --clean-first --parallel 4 --verbose"
  },
  "environment": {
    "os": "Windows-11-10.0.22631-SP0",
    "machine": "AMD64",
    "python": "3.13.5 (tags/v3.13.5:6cb20a2, Jun 11 2025, 16:15:46) [MSC v.1943 64 bit (AMD64)]",
    "host_before": {
      "cpu_load_percent": 1,
      "logical_processors": 12,
      "visible_ram_kib": 33387800,
      "free_ram_kib": 15642268
    },
    "host_after": {
      "cpu_load_percent": 0,
      "logical_processors": 12,
      "visible_ram_kib": 33387800,
      "free_ram_kib": 15639804
    },
    "concurrent_work_note": "Before measurement, a 5-second CPU-time check showed no activity delta in three residual MSBuild processes and zero cl.exe processes. Pre/post Windows processor load and available RAM are captured; unrelated background work cannot be excluded.",
    "trial_policy": "one warmup per case and method; seven measured repetitions per case; baseline and basis-reuse order alternated each round; fresh workspace per invocation",
    "timing_scope": "steady_clock around reduce_hull or reduce_hull_basis_reuse only; point cloud setup, HiGHS LP workspace creation, and post-timing validation excluded",
    "comparison_status": "descriptive paired timings; no speedup/winner claim; no separate limiter profile"
  },
  "fixtures": [
    {
      "case_id": "permuted",
      "points": 10,
      "description": "permuted square corners, edge points and interior points"
    },
    {
      "case_id": "degenerate",
      "points": 7,
      "description": "full-dimensional square with a duplicate corner and edge points"
    },
    {
      "case_id": "interior-basis",
      "points": 5,
      "description": "center geometric interior point at ID 0 plus square corners"
    }
  ],
  "oracle": "Every warmup and measured result is complete, has unique retained IDs in range, and contains every original input point by independent HiGHS LP membership checks. For each timed pair, this is checked for both exact outputs produced inside the timed calls, after timing ends; mutual output containment is also checked. The deterministic interior fixture has a completed baseline and basis-reuse structural basis IDs [0, 3, 4], including center ID 0. The harness self-test exercises valid, duplicate and out-of-range ID sets and positive/negative input-containment cases.",
  "process": {
    "exit_code": 0,
    "invalid_stdout_lines": [],
    "rows": 48,
    "measured_rows": 42,
    "warmup_rows": 6,
    "failures": 0,
    "stderr_sha256": "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855"
  },
  "trials": [
    {
      "round": 0,
      "case_id": "permuted",
      "method": "baseline",
      "warmup": true,
      "elapsed_ns": 960500,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 10,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 6,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        0,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 0,
      "case_id": "permuted",
      "method": "basis-reuse",
      "warmup": true,
      "elapsed_ns": 76100,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 7,
      "bulk_removals": 2,
      "retained": 8,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4,
        5,
        7,
        8
      ],
      "basis_points": [
        4,
        3,
        1
      ]
    },
    {
      "round": 0,
      "case_id": "degenerate",
      "method": "baseline",
      "warmup": true,
      "elapsed_ns": 636200,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 7,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 3,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 0,
      "case_id": "degenerate",
      "method": "basis-reuse",
      "warmup": true,
      "elapsed_ns": 49800,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 4,
      "bulk_removals": 2,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        5
      ],
      "basis_points": [
        2,
        3,
        0
      ]
    },
    {
      "round": 0,
      "case_id": "interior-basis",
      "method": "baseline",
      "warmup": true,
      "elapsed_ns": 459300,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 5,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 1,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 0,
      "case_id": "interior-basis",
      "method": "basis-reuse",
      "warmup": true,
      "elapsed_ns": 45300,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 2,
      "bulk_candidates": 2,
      "bulk_removals": 0,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4
      ],
      "basis_points": [
        0,
        3,
        4
      ]
    },
    {
      "round": 1,
      "case_id": "permuted",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 926600,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 10,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 6,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        0,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 1,
      "case_id": "permuted",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 54300,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 7,
      "bulk_removals": 2,
      "retained": 8,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4,
        5,
        7,
        8
      ],
      "basis_points": [
        4,
        3,
        1
      ]
    },
    {
      "round": 1,
      "case_id": "degenerate",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 660100,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 7,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 3,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 1,
      "case_id": "degenerate",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 48800,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 4,
      "bulk_removals": 2,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        5
      ],
      "basis_points": [
        2,
        3,
        0
      ]
    },
    {
      "round": 1,
      "case_id": "interior-basis",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 459600,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 5,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 1,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 1,
      "case_id": "interior-basis",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 43500,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 2,
      "bulk_candidates": 2,
      "bulk_removals": 0,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4
      ],
      "basis_points": [
        0,
        3,
        4
      ]
    },
    {
      "round": 2,
      "case_id": "permuted",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 59300,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 7,
      "bulk_removals": 2,
      "retained": 8,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4,
        5,
        7,
        8
      ],
      "basis_points": [
        4,
        3,
        1
      ]
    },
    {
      "round": 2,
      "case_id": "permuted",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 919800,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 10,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 6,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        0,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 2,
      "case_id": "degenerate",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 51300,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 4,
      "bulk_removals": 2,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        5
      ],
      "basis_points": [
        2,
        3,
        0
      ]
    },
    {
      "round": 2,
      "case_id": "degenerate",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 648800,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 7,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 3,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 2,
      "case_id": "interior-basis",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 45600,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 2,
      "bulk_candidates": 2,
      "bulk_removals": 0,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4
      ],
      "basis_points": [
        0,
        3,
        4
      ]
    },
    {
      "round": 2,
      "case_id": "interior-basis",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 489600,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 5,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 1,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 3,
      "case_id": "permuted",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 899400,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 10,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 6,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        0,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 3,
      "case_id": "permuted",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 52800,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 7,
      "bulk_removals": 2,
      "retained": 8,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4,
        5,
        7,
        8
      ],
      "basis_points": [
        4,
        3,
        1
      ]
    },
    {
      "round": 3,
      "case_id": "degenerate",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 643600,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 7,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 3,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 3,
      "case_id": "degenerate",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 48400,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 4,
      "bulk_removals": 2,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        5
      ],
      "basis_points": [
        2,
        3,
        0
      ]
    },
    {
      "round": 3,
      "case_id": "interior-basis",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 467300,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 5,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 1,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 3,
      "case_id": "interior-basis",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 43100,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 2,
      "bulk_candidates": 2,
      "bulk_removals": 0,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4
      ],
      "basis_points": [
        0,
        3,
        4
      ]
    },
    {
      "round": 4,
      "case_id": "permuted",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 54300,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 7,
      "bulk_removals": 2,
      "retained": 8,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4,
        5,
        7,
        8
      ],
      "basis_points": [
        4,
        3,
        1
      ]
    },
    {
      "round": 4,
      "case_id": "permuted",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 993900,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 10,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 6,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        0,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 4,
      "case_id": "degenerate",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 52200,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 4,
      "bulk_removals": 2,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        5
      ],
      "basis_points": [
        2,
        3,
        0
      ]
    },
    {
      "round": 4,
      "case_id": "degenerate",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 642400,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 7,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 3,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 4,
      "case_id": "interior-basis",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 44200,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 2,
      "bulk_candidates": 2,
      "bulk_removals": 0,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4
      ],
      "basis_points": [
        0,
        3,
        4
      ]
    },
    {
      "round": 4,
      "case_id": "interior-basis",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 461000,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 5,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 1,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 5,
      "case_id": "permuted",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 893400,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 10,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 6,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        0,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 5,
      "case_id": "permuted",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 52000,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 7,
      "bulk_removals": 2,
      "retained": 8,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4,
        5,
        7,
        8
      ],
      "basis_points": [
        4,
        3,
        1
      ]
    },
    {
      "round": 5,
      "case_id": "degenerate",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 644600,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 7,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 3,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 5,
      "case_id": "degenerate",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 50600,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 4,
      "bulk_removals": 2,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        5
      ],
      "basis_points": [
        2,
        3,
        0
      ]
    },
    {
      "round": 5,
      "case_id": "interior-basis",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 474900,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 5,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 1,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 5,
      "case_id": "interior-basis",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 43200,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 2,
      "bulk_candidates": 2,
      "bulk_removals": 0,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4
      ],
      "basis_points": [
        0,
        3,
        4
      ]
    },
    {
      "round": 6,
      "case_id": "permuted",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 55100,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 7,
      "bulk_removals": 2,
      "retained": 8,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4,
        5,
        7,
        8
      ],
      "basis_points": [
        4,
        3,
        1
      ]
    },
    {
      "round": 6,
      "case_id": "permuted",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 917400,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 10,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 6,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        0,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 6,
      "case_id": "degenerate",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 54000,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 4,
      "bulk_removals": 2,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        5
      ],
      "basis_points": [
        2,
        3,
        0
      ]
    },
    {
      "round": 6,
      "case_id": "degenerate",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 646800,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 7,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 3,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 6,
      "case_id": "interior-basis",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 50300,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 2,
      "bulk_candidates": 2,
      "bulk_removals": 0,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4
      ],
      "basis_points": [
        0,
        3,
        4
      ]
    },
    {
      "round": 6,
      "case_id": "interior-basis",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 492100,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 5,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 1,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 7,
      "case_id": "permuted",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 872000,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 10,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 6,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        0,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 7,
      "case_id": "permuted",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 52400,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 7,
      "bulk_removals": 2,
      "retained": 8,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4,
        5,
        7,
        8
      ],
      "basis_points": [
        4,
        3,
        1
      ]
    },
    {
      "round": 7,
      "case_id": "degenerate",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 623100,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 7,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 3,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 7,
      "case_id": "degenerate",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 49900,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 0,
      "bulk_candidates": 4,
      "bulk_removals": 2,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        5
      ],
      "basis_points": [
        2,
        3,
        0
      ]
    },
    {
      "round": 7,
      "case_id": "interior-basis",
      "method": "baseline",
      "warmup": false,
      "elapsed_ns": 474700,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 5,
      "basis_solves": 0,
      "pivots": 0,
      "degenerate_pivots": 0,
      "bulk_candidates": 0,
      "bulk_removals": 1,
      "retained": 4,
      "fallback": false,
      "retained_points": [
        1,
        2,
        3,
        4
      ],
      "basis_points": []
    },
    {
      "round": 7,
      "case_id": "interior-basis",
      "method": "basis-reuse",
      "warmup": false,
      "elapsed_ns": 45900,
      "status": "complete",
      "verified": true,
      "output_ids_valid": true,
      "contains_all_inputs": true,
      "lp_calls": 0,
      "basis_solves": 1,
      "pivots": 4,
      "degenerate_pivots": 2,
      "bulk_candidates": 2,
      "bulk_removals": 0,
      "retained": 5,
      "fallback": false,
      "retained_points": [
        0,
        1,
        2,
        3,
        4
      ],
      "basis_points": [
        0,
        3,
        4
      ]
    }
  ],
  "summary": [
    {
      "case_id": "degenerate",
      "method": "baseline",
      "attempts": 7,
      "successes": 7,
      "failures": 0,
      "median_ns": 644600,
      "min_ns": 623100,
      "max_ns": 660100,
      "median_membership_lp_calls": 7,
      "median_basis_solves": 0,
      "median_pivots": 0,
      "median_degenerate_pivots": 0,
      "median_bulk_candidates": 0,
      "median_bulk_removals": 3
    },
    {
      "case_id": "degenerate",
      "method": "basis-reuse",
      "attempts": 7,
      "successes": 7,
      "failures": 0,
      "median_ns": 50600,
      "min_ns": 48400,
      "max_ns": 54000,
      "median_membership_lp_calls": 0,
      "median_basis_solves": 1,
      "median_pivots": 4,
      "median_degenerate_pivots": 0,
      "median_bulk_candidates": 4,
      "median_bulk_removals": 2
    },
    {
      "case_id": "interior-basis",
      "method": "baseline",
      "attempts": 7,
      "successes": 7,
      "failures": 0,
      "median_ns": 474700,
      "min_ns": 459600,
      "max_ns": 492100,
      "median_membership_lp_calls": 5,
      "median_basis_solves": 0,
      "median_pivots": 0,
      "median_degenerate_pivots": 0,
      "median_bulk_candidates": 0,
      "median_bulk_removals": 1
    },
    {
      "case_id": "interior-basis",
      "method": "basis-reuse",
      "attempts": 7,
      "successes": 7,
      "failures": 0,
      "median_ns": 44200,
      "min_ns": 43100,
      "max_ns": 50300,
      "median_membership_lp_calls": 0,
      "median_basis_solves": 1,
      "median_pivots": 4,
      "median_degenerate_pivots": 2,
      "median_bulk_candidates": 2,
      "median_bulk_removals": 0
    },
    {
      "case_id": "permuted",
      "method": "baseline",
      "attempts": 7,
      "successes": 7,
      "failures": 0,
      "median_ns": 917400,
      "min_ns": 872000,
      "max_ns": 993900,
      "median_membership_lp_calls": 10,
      "median_basis_solves": 0,
      "median_pivots": 0,
      "median_degenerate_pivots": 0,
      "median_bulk_candidates": 0,
      "median_bulk_removals": 6
    },
    {
      "case_id": "permuted",
      "method": "basis-reuse",
      "attempts": 7,
      "successes": 7,
      "failures": 0,
      "median_ns": 54300,
      "min_ns": 52000,
      "max_ns": 59300,
      "median_membership_lp_calls": 0,
      "median_basis_solves": 1,
      "median_pivots": 4,
      "median_degenerate_pivots": 0,
      "median_bulk_candidates": 7,
      "median_bulk_removals": 2
    }
  ]
}