{ "schema": 1, "captured_on": "2026-07-31", "checkpoint": "exact-rational-bezier-parallel-carrier", "source_revision": "8284dcfb8bbbbaebdc955822e42cb753aa28af5d", "implementation_revisions": [ "8284dcf" ], "historical_control_revision": "92b9477b43bd2912802a50a9be8b6066b976eb54", "frozen_baseline": "../baselines/2026-07-31/baseline.json", "scope": { "carrier": "BezierParallel2 is one machine word and clone-shares one immutable source/distance record plus lazy polynomial-basis and homogeneous-tangent caches", "native_polynomial_fast_path": "quadratic and cubic sources remain native instead of being eagerly promoted to general rational control storage", "rational_coverage": "RationalQuadraticBezier2 and arbitrary-degree RationalBezier2 expose exact left/right parallel carriers", "curve_path_admission": "certified CurvePath2 parallel construction admits regular exact rational-PH spans without source chords", "circle_fast_path": "one shared rational circular-conic recognizer materializes same-parameter concentric degree-two curves, including exact radius collapse and negative-radius reversal", "compatibility_shims_added": false, "hypermesh_modified": false }, "exactness_and_policy": { "homogeneous_source": "P=(X/W,Y/W)", "homogeneous_tangent": "H=(X'W-XW',Y'W-YW')", "parallel": "Q=P+d*R90(H)/sqrt(H dot H)", "derivative": "Q'=H/W^2+d*(R90(H')/S-R90(H)*(H dot H')/S^3), S=sqrt(H dot H)", "cusp_equation": "d*W^2*(H' cross H)+S^3=0; roots of the squared polynomial are isolated exactly and opposite-sign roots are rejected", "projective_boundary": "all roots of W on the closed unit interval are rejected before evaluation, singularity analysis, or exact materialization", "ph_materialization": "when H dot H=S^2, the exact homogeneous parallel is (XS-dW*Hy,YS+dW*Hx,WS)", "bernstein_completion": "strict positivity of WS is first certified on [0,1], then exact incremental degree elevation continues until every weight coefficient is positive; the former arbitrary +32 cap is deleted", "strict": "STRICT requires exact sign, root, square, regularity, and branch evidence and never substitutes a finite approximation", "approximate_512": "APPROXIMATE_512 uses the same exact carrier and may terminate only an unresolved equality/sign predicate at the inherited 512-bit terminal", "endpoint_identity": "structural t=0 and t=1 rational evaluations return the retained exact endpoints directly", "common_circle_center": "independently authored algebraic circular conics recover the minimal tangent-normal center and validate it against the implicit conic" }, "regression_matrix": { "focused_test_target": "tests/hypercurve_bezier_fit_offset.rs", "test_count": 38, "all_features": "pass", "no_default_features": "pass", "covered_paths": [ "polynomial quadratic and cubic analytic point/derivative evaluation", "source singularities and represented/nonrepresented offset cusps", "nonuniform rational line same-parameter materialization", "noncircular arbitrary-degree rational PH point and derivative replay", "rational quarter circles with rational and algebraic weights", "circle radius collapse and negative-scale reversal", "projective denominator boundary rejection", "regular rational PH CurvePath promotion without chord fallback", "STRICT and APPROXIMATE_512 materialization", "strictly positive PH speed requiring Bernstein degree 65, beyond the deleted fixed search cap" ] }, "paired_release_carrier_benchmark": { "command": "taskset -c 9 HYPERCURVE_OFFSET_BENCH_GROUP=bezier-carrier {historical,candidate target/release/deps/offset-4d7476685f053fc3}", "method": "15 alternating historical/candidate process pairs after warmup; medians of fixed-iteration native release runs", "construction": { "iterations_per_process": 100000, "historical_nanoseconds_per_iteration": [2127.43678, 1629.43249, 1587.93203, 1549.78565, 1572.05252, 1604.87597, 1640.92, 1594.07901, 1591.3955, 1639.45471, 1581.30609, 1584.38177, 1566.22162, 1600.90634, 1609.15057], "candidate_nanoseconds_per_iteration": [193.82373, 252.27842, 65.96898, 75.35164, 62.93599, 68.5188, 62.45432, 64.86716, 65.33383, 67.96755, 61.84437, 62.93619, 67.42968, 64.64457, 66.50884], "historical_median_nanoseconds": 1594.07901, "candidate_median_nanoseconds": 65.96898, "median_change_percent": -95.861624, "interpretation": "native source retention and lazy clone-shared differential construction remove eager power-basis work" }, "evaluation": { "iterations_per_process": 10000, "historical_nanoseconds_per_iteration": [5284.214, 5200.6908, 5161.9774, 5184.3719, 5200.5078, 5184.1769, 5211.398, 5297.5582, 5166.0001, 5303.5377, 5527.4004, 5137.5801, 5171.8048, 5224.4072, 5131.8195], "candidate_nanoseconds_per_iteration": [4824.2296, 3935.4805, 3948.8865, 4108.6455, 4090.8638, 3995.9653, 4360.5713, 4091.2777, 3956.2431, 4018.7977, 4025.1313, 3914.7059, 3869.9339, 3970.043, 3938.0853], "historical_median_nanoseconds": 5200.5078, "candidate_median_nanoseconds": 3995.9653, "median_change_percent": -23.162017, "interpretation": "one lazy differential is shared across all repeated exact evaluations" }, "ph_materialization": { "iterations_per_process": 1000, "historical_nanoseconds_per_iteration": [16751.572, 16231.719, 15804.547, 15645.419, 15990.215, 16417.256, 15593.362, 16090.738, 15759.71, 15921.67, 15762.241, 15781.289, 16036.642, 16126.095, 15776.799], "candidate_nanoseconds_per_iteration": [15898.591, 15737.832, 15658.118, 16352.68, 16017.243, 15932.269, 15616.08, 17041.892, 15695.445, 15745.651, 15695.045, 15737.642, 16713.386, 15888.732, 15710.664], "historical_median_nanoseconds": 15921.67, "candidate_median_nanoseconds": 15745.651, "median_change_percent": -1.105531, "interpretation": "the generalized homogeneous PH path and completeness fix remain throughput-neutral on the historical polynomial fixture" } }, "competitive_open_cubic": { "command": "taskset -c 9 HYPERCURVE_COMPARE_GROUP=bezier_offset/open_cubic {historical,candidate comparative-b2bf500a69174bc4}", "method": "seven alternating process pairs; each process reports the median of seven approximately 75 ms samples", "historical_process_medians_nanoseconds": { "hypercurve_certified": [31414738.3, 29917297.7, 29955321.3, 32892393.7, 29835526.3, 30136386.0, 30155394.3], "hypercurve_chord_fallback": [948795.3, 924843.0, 922829.6, 933257.8, 921039.0, 928084.0, 932560.3], "curvo_heuristic": [14843.9, 8180.8, 8258.9, 8242.3, 8222.9, 8465.5, 8432.4] }, "candidate_process_medians_nanoseconds": { "hypercurve_certified": [30434280.5, 29889059.3, 29779950.0, 29708915.0, 29719124.0, 29667394.7, 29471561.0], "hypercurve_chord_fallback": [1266739.5, 919796.9, 918315.8, 914728.8, 913561.9, 927281.7, 910283.9], "curvo_heuristic": [8242.8, 8337.2, 8299.3, 8300.7, 8285.4, 8223.8, 8316.5] }, "historical_medians_nanoseconds": { "hypercurve_certified": 30136386.0, "hypercurve_chord_fallback": 928084.0, "curvo_heuristic": 8258.9 }, "candidate_medians_nanoseconds": { "hypercurve_certified": 29719124.0, "hypercurve_chord_fallback": 918315.8, "curvo_heuristic": 8299.3 }, "median_change_percent": { "hypercurve_certified": -1.384579, "hypercurve_chord_fallback": -1.052512, "curvo_heuristic": 0.489169 }, "contract_note": "Hypercurve certified proves an exact-scalar conservative parallel bound; the chord and Curvo controls use weaker finite/heuristic guarantees and are not interchangeable correctness peers" }, "heaptrack": { "construction_100000": { "historical_allocation_calls": 4300074, "candidate_allocation_calls": 100040, "allocation_change_percent": -97.673528, "historical_temporary_allocations": 800002, "candidate_temporary_allocations": 100002, "temporary_change_percent": -87.499781, "historical_peak_heap_kib": 79.22, "candidate_peak_heap_kib": 76.87, "peak_change_percent": -2.966423, "historical_leaked_kib": 4.00, "candidate_leaked_kib": 1.65 }, "evaluation_10000": { "historical_allocation_calls": 1050291, "candidate_allocation_calls": 760369, "allocation_change_percent": -27.603969, "historical_temporary_allocations": 120010, "candidate_temporary_allocations": 120012, "historical_peak_heap_kib": 89.53, "candidate_peak_heap_kib": 90.56, "peak_change_percent": 1.150452, "historical_leaked_kib": 12.42, "candidate_leaked_kib": 13.79, "interpretation": "recurring allocation calls fall materially; the 1.03 KiB peak increase is the retained lazy source/differential cache and remains a visible memory sentinel" } }, "release_size": { "artifact": "matched offset release benchmark executable", "historical_file_bytes": 6399032, "candidate_file_bytes": 6454520, "file_change_bytes": 55488, "file_change_percent": 0.867131, "historical_text_bytes": 4825602, "candidate_text_bytes": 4882630, "text_change_bytes": 57028, "text_change_percent": 1.181780, "historical_elf_load_file_bytes": 5086080, "candidate_elf_load_file_bytes": 5143784, "elf_load_change_bytes": 57704, "elf_load_change_percent": 1.134548, "interpretation": "accepted first-cut size cost for arbitrary-degree rational exactness, policy regressions, and removal of a mathematical completeness cap; later shared polynomial kernels and piecewise low-degree PH publication remain size/memory optimization targets" }, "static_call_graph": { "tool": "tools/hyper-callgraph", "source_only_historical": { "nodes": 17003, "edges": 28734 }, "source_only_candidate": { "nodes": 17131, "edges": 29002 }, "candidate_hypersolve_source_only": { "nodes": 4162, "edges": 6671 }, "workspace_union_navigation_scan": { "nodes": 21365, "edges": 35900, "hypercurve_nodes": 17202, "hypersolve_nodes": 4163, "best_effort_cross_library_edges": 3 }, "caveat": "the parser is a static approximation; the historical source-only delta also includes accepted Boolean cuts between 92b9477 and this checkpoint, while the workspace-union navigation scan includes staged historical repository copies and is not a size delta" }, "validation": { "cargo_test_all_features": "pass: 274 library tests, every integration target, retained adversarial Boolean corpora, and doc tests", "focused_all_features": "pass: 38/38", "focused_no_default_features": "pass: 38/38", "clippy_all_targets_all_features_deny_warnings": "pass", "clippy_all_targets_no_default_features_deny_warnings": "pass", "cargo_fmt_check": "pass", "git_diff_check": "pass" }, "next_boundary": { "correctness": "add split/reversal/subcurve/bounds/incidence/intersection support directly to the exact general parallel carrier, then feed its raw pieces into the authoritative arrangement", "memory": "replace pathological high-degree positive-weight PH publication with exact low-degree piecewise spans when subdivision is smaller", "topology": "generate round, bevel, and bounded-miter joins under an explicit OffsetCornerStyle2 and regularize signed material/hole offsets through CurveRegionBooleanContext", "hypersolve": "add only reusable implicitization, resultant factor filtering, and exact root replay primitives needed by non-PH parallel intersections" } }