{
  "schema": 1,
  "captured_on": "2026-07-31",
  "checkpoint": "overlap-parameter-correspondence",
  "source_revision": "3d4bef2e1c202ad81370ed3da940c80844bb6706",
  "historical_control_revision": "82c1eea62fe5dafb5fba9df36b03a2794225cfee",
  "frozen_baseline": "../baselines/2026-07-31/baseline.json",
  "scope": {
    "closed_boundaries": [
      "retained CurveRegion2 operands may clip the same conic image through a non-affine Mobius parameter correspondence",
      "retained CurveRegion2 operands may clip the same line image through independently nonlinear monotone polynomial parameterizations",
      "forward and reversed parameter traversal retain oriented overlap ranges",
      "STRICT and APPROXIMATE_512 use the same exact returned parameters and geometry"
    ],
    "authoritative_engine": "all nonempty, nonidentical all-family Boolean batches continue through one CurveRegion2 arrangement",
    "unchanged_fast_path": "degree-aligned identity and unit-complement overlap transports remain in the compact affine clip path",
    "public_api_growth": false,
    "compatibility_shims_added": false
  },
  "defects_closed": {
    "mobius_retained_overlap": "the historical engine returned Blocked(Boolean, QuadraticBezier, Unsupported)",
    "nonlinear_line_retained_overlap": "the historical engine returned Blocked(Boolean, RationalBezier, Unsupported)",
    "reversed_complete_control_net_overlap": "the second overlap range now reports 1 to 0, matching documented traversal orientation, instead of 0 to 1"
  },
  "exact_correspondence_architecture": {
    "retention": "one private correspondence witness is classified when top-level overlap evidence is formed and retained only by CurveIntersectionOverlap2",
    "public_equality": "the private witness is intentionally excluded from CurveIntersectionOverlap2 public PartialEq semantics",
    "witness_variants": [
      "identity",
      "exact unit complement 1 - t",
      "general clone-shared RationalBezier2 carrier pair with retained uncertainty"
    ],
    "general_transport_order": [
      "implicit-conic rational parameter map",
      "exact affine polynomial-graph parameter map",
      "exact point incidence for represented source parameters",
      "certified injective-axis algebraic transport"
    ],
    "injective_axis_transport": [
      "Hypersolve maps the source parameter's exact algebraic root through the selected rational coordinate",
      "Hypercurve forms the target coordinate preimage polynomial exactly",
      "all target roots on [0,1] are isolated",
      "exact algebraic coordinate equality selects one and only one target parameter"
    ],
    "clipping": "the first retained carrier interval is clipped, its endpoints are transported, and the reverse map is evaluated only if the second retained carrier clips that mapped interval further",
    "exactness": "no algebraic root, coordinate, or returned carrier is replaced by a finite approximation",
    "policy": "unresolved comparisons remain typed STRICT blockers; APPROXIMATE_512 may terminate only predicate equality through the inherited policy and reports consumption at the public outcome boundary"
  },
  "regression_matrix": {
    "mobius_conic": {
      "weights": [1, 2, 4],
      "directions": ["forward", "reversed"],
      "policies": ["STRICT", "APPROXIMATE_512"],
      "operations": ["union", "intersection", "difference", "xor"],
      "result": "pass"
    },
    "independently_nonlinear_line": {
      "first_coordinate": "x(t) = 2t + 2t^2",
      "second_coordinate": "x(s) = 6s - 2s^2",
      "directions": ["forward", "reversed"],
      "policies": ["STRICT", "APPROXIMATE_512"],
      "operations": ["union", "intersection", "difference", "xor"],
      "result": "pass"
    }
  },
  "historical_completion": {
    "method": "the final benchmark harness was copied into an isolated 82c1eea source snapshot and built against the same dependency state and toolchain",
    "aligned_conic_overlap": "historical and candidate engines complete",
    "mobius_overlap": "historical engine panics after Blocked(Boolean, QuadraticBezier, Unsupported); candidate completes",
    "nonlinear_line_overlap": "historical engine panics after Blocked(Boolean, RationalBezier, Unsupported); candidate completes",
    "interpretation": "the two principal fixtures measure newly supported mathematical paths rather than a slower replacement for historical successful behavior"
  },
  "paired_release_pathological_benchmark": {
    "command": "taskset -c 9 HYPERCURVE_PATHOLOGICAL_MODE=boolean {historical,candidate pathological_regions binary}",
    "method": "eleven alternating-order process pairs; complete 67-cell all-family workload; same dependency state and toolchain",
    "cells_per_process": 67,
    "historical_milliseconds": [
      486.332823,
      481.079761,
      482.411080,
      479.727024,
      482.188476,
      486.017373,
      479.707785,
      484.546694,
      491.508968,
      488.910486,
      501.529382
    ],
    "candidate_milliseconds": [
      494.724298,
      481.859738,
      485.978196,
      493.628193,
      485.602482,
      487.998908,
      494.378161,
      486.776722,
      486.144785,
      490.970285,
      484.550024
    ],
    "historical_median_milliseconds": 484.546694,
    "candidate_median_milliseconds": 486.776722,
    "median_change_percent": 0.460230,
    "paired_geometric_mean_change_percent": 0.540440,
    "interpretation": "the complete all-family workload remains throughput-neutral"
  },
  "aligned_supported_path_benchmark": {
    "fixture": "aligned-conic-overlap",
    "method": "eleven alternating-order CPU-9 process pairs; 2000 all-four batches per process",
    "historical_nanoseconds_per_batch": [
      349853,
      359923,
      358152,
      354843,
      367852,
      354829,
      352074,
      359368,
      355012,
      350646,
      349355
    ],
    "candidate_nanoseconds_per_batch": [
      360816,
      368082,
      353126,
      357754,
      351502,
      359010,
      360213,
      355146,
      361049,
      360954,
      353204
    ],
    "historical_median_nanoseconds": 354843,
    "candidate_median_nanoseconds": 359010,
    "median_change_percent": 1.174322,
    "paired_geometric_mean_change_percent": 0.742618,
    "fragment_counts": {
      "independent": [4, 2, 0, 4],
      "shared": [4, 2, 0, 4]
    },
    "interpretation": "the already-supported projectively aligned lane stays on its compact fast path; the small retained-witness cost is accepted"
  },
  "new_path_batch_benchmarks": {
    "method": "eleven alternating CPU-9 independent/shared processes using the same final binary; independent performs four authoritative single-operation calls and shared performs one all-four arrangement",
    "mobius_overlap": {
      "iterations_per_process": 200,
      "independent_nanoseconds_per_batch": [
        4576800,
        4550096,
        4438232,
        4432841,
        4431844,
        4455224,
        4551374,
        4494269,
        4570611,
        4495629,
        4456268
      ],
      "shared_nanoseconds_per_batch": [
        1156482,
        1112207,
        1122449,
        1107604,
        1119365,
        1127864,
        1162984,
        1149549,
        1120523,
        1110129,
        1114333
      ],
      "independent_median_nanoseconds": 4494269,
      "shared_median_nanoseconds": 1120523,
      "shared_speedup": 4.010867,
      "fragment_counts": {
        "independent": [4, 2, 0, 4],
        "shared": [4, 2, 0, 4]
      },
      "historical_status": "unsupported"
    },
    "nonlinear_line_overlap": {
      "iterations_per_process": 1000,
      "independent_nanoseconds_per_batch": [
        84522,
        95661,
        84360,
        88447,
        89845,
        86055,
        85028,
        86561,
        88831,
        88182,
        84112
      ],
      "shared_nanoseconds_per_batch": [
        220152,
        230109,
        220718,
        215173,
        214889,
        212019,
        213676,
        218299,
        213665,
        218894,
        214819
      ],
      "independent_median_nanoseconds": 86561,
      "shared_median_nanoseconds": 215173,
      "shared_slowdown": 2.485796,
      "fragment_counts": {
        "independent": [4, 4, 0, 4],
        "shared": [6, 4, 0, 4]
      },
      "historical_status": "unsupported",
      "interpretation": "four independent calls re-promote exact line images into the mature native line kernel, while the shared arrangement retains general rational carriers; native line publication inside the unified authority is the measured optimization target"
    }
  },
  "heaptrack": {
    "all_family": {
      "command": "HYPERCURVE_PATHOLOGICAL_MODE=boolean heaptrack --record-only {historical,candidate pathological_regions binary}",
      "historical_allocation_calls": 8227180,
      "candidate_allocation_calls": 8227180,
      "historical_temporary_allocations": 1380711,
      "candidate_temporary_allocations": 1380711,
      "historical_peak_heap": "34.70M",
      "candidate_peak_heap": "34.70M",
      "historical_peak_rss": "65.04M",
      "candidate_peak_rss": "65.15M",
      "historical_total_leaked": "476.82K",
      "candidate_total_leaked": "476.82K",
      "interpretation": "allocation and temporary-allocation counts are exactly unchanged; the RSS difference is process noise"
    },
    "mobius_200_batches": {
      "independent_allocation_calls": 13956097,
      "shared_allocation_calls": 3572697,
      "allocation_reduction_percent": 74.400457,
      "allocation_ratio": 3.906320,
      "independent_temporary_allocations": 718563,
      "shared_temporary_allocations": 183963,
      "independent_peak_heap": "543.52K",
      "shared_peak_heap": "543.52K"
    },
    "nonlinear_line_1000_batches": {
      "independent_allocation_calls": 391058,
      "shared_allocation_calls": 2077060,
      "shared_allocation_increase_percent": 431.138603,
      "shared_to_independent_allocation_ratio": 5.311386,
      "independent_temporary_allocations": 17373,
      "shared_temporary_allocations": 151372,
      "independent_peak_heap": "234.61K",
      "shared_peak_heap": "235.64K"
    },
    "artifacts": [
      "/tmp/hypercurve-correspondence-parent.zst.zst",
      "/tmp/hypercurve-correspondence-candidate-3d4.zst.zst",
      "/tmp/hypercurve-mobius-independent-3d4.zst.zst",
      "/tmp/hypercurve-mobius-shared-3d4.zst.zst",
      "/tmp/hypercurve-line-independent-3d4.zst.zst",
      "/tmp/hypercurve-line-shared-3d4.zst.zst"
    ]
  },
  "matched_release_pathological_binary": {
    "command": "cargo bench --bench pathological_regions --no-run; size; strip --strip-all",
    "historical_debug_file_bytes": 7220360,
    "candidate_debug_file_bytes": 7231656,
    "debug_file_delta_bytes": 11296,
    "debug_file_delta_percent": 0.156446,
    "historical_stripped_file_bytes": 5736328,
    "candidate_stripped_file_bytes": 5750384,
    "stripped_file_delta_bytes": 14056,
    "stripped_file_delta_percent": 0.245035,
    "historical_size": {
      "text": 5466518,
      "data": 265928,
      "bss": 3856,
      "total_loadable": 5736302
    },
    "candidate_size": {
      "text": 5480346,
      "data": 266160,
      "bss": 2088,
      "total_loadable": 5748594
    },
    "text_delta_bytes": 13828,
    "data_delta_bytes": 232,
    "bss_delta_bytes": -1768,
    "total_loadable_delta_bytes": 12292,
    "total_loadable_delta_percent": 0.214284,
    "interpretation": "the sub-quarter-percent linked-size cost buys exact completion of two historically unsupported overlap classes"
  },
  "static_callgraph": {
    "command": "/home/tim/Documents/GitHub/workspace/tools/hyper-callgraph/target/release/hyper-callgraph --root {isolated source root} --out-dir /tmp/hypercurve-overlap-correspondence-callgraph --crate-name hypercurve --include-examples --include-tests --include-bench --include-fuzz --format json",
    "historical_nodes": 22977,
    "candidate_nodes": 23032,
    "node_delta": 55,
    "historical_edges": 39639,
    "candidate_edges": 39783,
    "edge_delta": 144,
    "artifact": "/tmp/hypercurve-overlap-correspondence-callgraph/callgraph.json",
    "interpretation": "the delta includes the two-policy, two-orientation integration matrix and three persistent benchmark fixtures in addition to the private exact transport"
  },
  "verification": {
    "unit_tests": "267/267 pass in 41.81 seconds",
    "focused_curve_region_boolean_tests": "22/22 pass in 3.79 seconds",
    "generated_curve_region_boolean_tests": "11/11 pass in 91.78 seconds",
    "cargo_clippy_all_features_all_targets_deny_warnings": "pass",
    "cargo_clippy_no_default_features_all_targets_deny_warnings": "pass",
    "cargo_check_no_default_features": "pass",
    "cargo_fmt": "pass",
    "git_diff_check": "pass",
    "hypermesh_modified_by_this_work": false
  },
  "remaining_boolean_boundary": {
    "unsupported_correspondence": "a shared component whose target carrier has no certified injective coordinate and no conic or polynomial-graph inverse still requires exact bivariate branch evidence",
    "lower_dimensional_ownership": "complete regularized ownership for all coincident, tangent, and zero-area remnants remains to be audited and closed",
    "performance": "fold exact native line and then line/arc publication into the authoritative arrangement so nonlinear line-image batches recover native compactness and allocation behavior",
    "later_phases": "general exact offsets and solver-driven fillet/chamfer remain pending"
  }
}