{ "schema": 1, "captured_on": "2026-07-31", "checkpoint": "projective-cubic-shared-component", "source_revision": "7a77d6815310a7e8cda44b1eeeab876ed3bdd561", "historical_control_revision": "ef7ddbce61806545b3d62ac3fa69ef25940330c0", "benchmark_harness_revision": "838fd30633f30836a819538acc1d08d3afd8a6bc", "hypersolve_revision": "b2a279032f4824c635923a6093fe1d342c208da9", "hypersolve_historical_control_revision": "963ed9b9dfb281d199a157e7e35ff30114b41079", "frozen_baseline": "../baselines/2026-07-31/baseline.json", "scope": { "closed_boundary": "retained regions may clip the same non-axis-monotone cubic image through an exact endpoint-fixed projective/Mobius parameter correspondence", "degree_scope": "the control-net certificate applies to every positive equal degree, not only cubics", "range_scope": "complete and partial oriented overlap ranges derive their maps from one retained scale and the already-retained ranges", "authoritative_engine": "all results continue through one CurveRegionBooleanContext arrangement", "public_api_growth": false, "compatibility_shims_added": false, "hypermesh_modified": false }, "defects_closed": { "non_axis_monotone_shared_cubic": "the historical engine returns Blocked(Boolean, CubicBezier, Boundary) after retained clipping removes every certified injective authored coordinate", "projective_subrange_transport": "trimmed carriers with geometrically scaled homogeneous weights now retain an exact range-local Mobius correspondence instead of falling into unsupported point replay", "rational_image_common_factor": "Hypersolve cancels an exact common numerator/denominator factor when it would otherwise make the image resultant vanish identically because of a source root outside the selected isolator" }, "exact_architecture": { "control_net_certificate": "affine control points must agree exactly in the selected orientation; nonzero common weight signs, a positive scale, and every geometric weight-ratio identity are policy-certified", "single_pass_classifier": "affine identity/unit-complement and projective relations are classified in one control-net pass per orientation; failed general candidates do not repeat point comparisons", "compact_correspondence": "EndpointProjective and RangeProjective each retain one Real scale plus orientation; partial-map coefficients are derived from retained overlap ranges on demand", "exact_parameter_map": "exact rational parameters use direct Real arithmetic; algebraic parameters use Hypersolve rational-image construction and exact candidate replay", "inverse": "the inverse 2x2 projective map is derived algebraically from the forward numerator and denominator and is tested in both orientations", "policy": "STRICT returns only certified relations; APPROXIMATE_512 may terminate inherited equality/sign predicates at 512 bits while returned parameters, carriers, and coordinates stay exact" }, "hypersolve_factor_cancellation": { "trigger": "exact nonconstant numerator and denominator polynomials", "method": "primitive integer polynomial GCD followed by exact quotient/remainder certification", "linear_fast_path": "two nonconstant linears skip GCD because they are either coprime or a constant rational map already handled by the existing proportionality test", "regression": "P=(x+3)(x^2-2), isolated positive sqrt(2), and x(x+3)/(x+3) transform exactly under STRICT and APPROXIMATE_512", "returned_geometry_approximated": false }, "regression_matrix": { "cubic_controls": [ [0, 0], [7, -5], [8, -4], [3, 3] ], "affine_frame": "u=3t and v=18t(1-t), proving image injectivity while both authored x and y reverse in the open domain", "projective_weights": [1, 2, 4, 8], "parameter_orientations": ["same", "reversed"], "overlap_scopes": ["complete", "partial retained subrange"], "policies": ["STRICT", "APPROXIMATE_512"], "operations": ["union", "intersection", "difference", "xor"], "intersection_evidence": { "contacts": 2, "overlaps": 1, "complete": true }, "result_fragment_counts": [4, 2, 0, 4], "result": "pass" }, "historical_completion": { "method": "the final benchmark harness was cherry-picked onto an isolated ef7ddbc source clone and both binaries were rebuilt against the same Hyperreal, Hyperlimit, and optimized Hypersolve state", "parent_exit_code": 101, "parent_error": "Blocked(Boolean, CubicBezier, Boundary)", "candidate_exit_code": 0, "candidate_fragment_counts": [4, 2, 0, 4], "interpretation": "the projective cubic row is newly supported mathematical coverage, not a slower replacement for a historically successful path" }, "paired_release_pathological_benchmark": { "command": "taskset -c 14 HYPERCURVE_PATHOLOGICAL_MODE=boolean {historical,candidate pathological_regions binary}", "method": "one warm-up followed by eleven alternating-order process pairs; complete 67-cell all-family workload; matched dependency state and toolchain", "cells_per_process": 67, "historical_milliseconds": [ 482.756673, 494.087467, 492.026458, 483.897365, 490.214461, 481.052870, 492.337847, 491.156038, 489.006085, 476.559407, 482.244748 ], "candidate_milliseconds": [ 490.841089, 499.803425, 488.330911, 482.214140, 484.217843, 491.886567, 487.898651, 492.223525, 484.304846, 480.547184, 493.171609 ], "historical_median_milliseconds": 489.006085, "candidate_median_milliseconds": 488.330911, "median_change_percent": -0.138071, "paired_geometric_mean_change_percent": 0.375620, "interpretation": "the complete all-family workload is throughput-neutral" }, "aligned_supported_path_benchmark": { "fixture": "aligned-conic-overlap", "command": "taskset -c 14 HYPERCURVE_CURVE_REGION_BATCH_ITERATIONS=2000 HYPERCURVE_CURVE_REGION_BATCH_MODE=shared {historical,candidate curve_region_boolean_batch binary}", "historical_nanoseconds_per_batch": [ 382425, 390099, 393914, 391306, 362309, 389720, 400292, 396613, 373638, 387345, 369008 ], "candidate_nanoseconds_per_batch": [ 386070, 378369, 381758, 401684, 400779, 390901, 394208, 386422, 377196, 373217, 382783 ], "historical_median_nanoseconds": 389720, "candidate_median_nanoseconds": 386070, "median_change_percent": -0.936570, "paired_geometric_mean_change_percent": 0.413117, "interpretation": "the already-supported shared-conic lane remains neutral" }, "new_projective_cubic_benchmark": { "command": "taskset -c 14 HYPERCURVE_CURVE_REGION_BATCH_FIXTURE=mobius-cubic-overlap HYPERCURVE_CURVE_REGION_BATCH_ITERATIONS=200 HYPERCURVE_CURVE_REGION_BATCH_MODE={independent,shared} candidate curve_region_boolean_batch binary", "method": "one warm-up followed by eleven alternating independent/shared processes; independent performs four authoritative calls and shared performs one all-four arrangement", "iterations_per_process": 200, "independent_nanoseconds_per_batch": [ 9172429, 9282519, 9129918, 9031595, 9104025, 9089821, 9135344, 9108300, 9301235, 9070990, 9176745 ], "shared_nanoseconds_per_batch": [ 2329013, 2319116, 2298047, 2302038, 2327402, 2321069, 2283979, 2379625, 2258903, 2290092, 2287414 ], "independent_median_nanoseconds": 9129918, "shared_median_nanoseconds": 2302038, "median_shared_speedup": 3.966015, "paired_geometric_mean_shared_speedup": 3.961449, "historical_status": "unsupported" }, "hypersolve_release_controls": { "method": "matched release Criterion binaries pinned to CPU 14; current shared dependency state; reported point estimates with confidence intervals", "linear_fractional_rational_image_microseconds": { "historical_interval": [7.9447, 8.0201, 8.1022], "candidate_interval": [8.0155, 8.0572, 8.0996], "point_estimate_change_percent": 0.462588, "interpretation": "overlapping intervals; statistically neutral" }, "degree_12_cubic_rational_image_milliseconds": { "historical_interval": [1.9418, 1.9500, 1.9585], "candidate_interval": [1.9190, 1.9274, 1.9372], "point_estimate_change_percent": -1.158974, "interpretation": "the higher-degree GCD-capable path does not regress" } }, "heaptrack": { "all_family": { "historical_allocation_calls": 8295412, "candidate_allocation_calls": 8295412, "historical_temporary_allocations": 1392519, "candidate_temporary_allocations": 1392519, "historical_peak_heap": "34.70M", "candidate_peak_heap": "34.70M", "historical_peak_rss": "65.03M", "candidate_peak_rss": "65.05M", "historical_total_leaked": "476.82K", "candidate_total_leaked": "476.82K", "interpretation": "allocation calls, temporary allocations, peak heap, and leaks are exactly unchanged" }, "projective_cubic_100_batches": { "independent_allocation_calls": 14243895, "shared_allocation_calls": 3711595, "allocation_reduction_percent": 73.942556, "allocation_ratio": 3.837675, "independent_temporary_allocations": 419323, "shared_temporary_allocations": 109423, "temporary_reduction_percent": 73.904842, "independent_peak_heap": "877.00K", "shared_peak_heap": "876.99K" }, "artifacts": [ "/tmp/hypercurve-projective-cubic-parent-b2-all-family.zst", "/tmp/hypercurve-projective-cubic-candidate-b2-all-family.zst", "/tmp/hypercurve-projective-cubic-b2-independent-100.zst", "/tmp/hypercurve-projective-cubic-b2-shared-100.zst" ] }, "matched_release_binaries": { "pathological": { "historical_file_bytes": 7028800, "candidate_file_bytes": 7044880, "file_delta_bytes": 16080, "file_delta_percent": 0.228773, "historical_stripped_bytes": 5589304, "candidate_stripped_bytes": 5605864, "stripped_delta_bytes": 16560, "stripped_delta_percent": 0.296280, "historical_text_bytes": 5319129, "candidate_text_bytes": 5335077, "text_delta_bytes": 15948, "historical_data_bytes": 266296, "candidate_data_bytes": 266920, "historical_bss_bytes": 3328, "candidate_bss_bytes": 3152, "historical_loadable_bytes": 5588753, "candidate_loadable_bytes": 5605149, "loadable_delta_bytes": 16396, "loadable_delta_percent": 0.293375 }, "curve_region_batch": { "historical_file_bytes": 6256152, "candidate_file_bytes": 6278264, "file_delta_bytes": 22112, "file_delta_percent": 0.353444, "historical_stripped_bytes": 4933952, "candidate_stripped_bytes": 4954704, "stripped_delta_bytes": 20752, "stripped_delta_percent": 0.420596, "historical_loadable_bytes": 4933285, "candidate_loadable_bytes": 4953761, "loadable_delta_bytes": 20476, "loadable_delta_percent": 0.415058 }, "interpretation": "the sub-half-percent linked-size cost is accepted for a new exact completion class; runtime remains the higher priority" }, "static_call_graph": { "command": "hyper-callgraph --root {snapshot} --crate-name hypercurve --include-examples --include-tests --include-bench --include-fuzz --format json", "historical_nodes": 23086, "candidate_nodes": 23136, "node_delta": 50, "historical_edges": 39896, "candidate_edges": 40006, "edge_delta": 110, "source_only_historical_nodes": 16957, "source_only_candidate_nodes": 17002, "source_only_node_delta": 45, "source_only_historical_edges": 28658, "source_only_candidate_edges": 28755, "source_only_edge_delta": 97, "historical_artifact": "/tmp/hypercurve-projective-cubic-callgraph-parent/callgraph.json", "candidate_artifact": "/tmp/hypercurve-projective-cubic-callgraph-candidate-final/callgraph.json" }, "competitive_context": { "rerun": false, "reason": "the available floating competitors do not expose exact retained rational-cubic Boolean topology or projective parameter correspondence, so no like-for-like completion row exists", "retained_reference": "the mixed-line/conic checkpoint records a 61.98x gap to Cavalier binary64 under explicitly unequal exactness and degeneracy guarantees", "interpretation": "historical failure plus absolute exact-path throughput is the honest comparison for this capability" }, "verification": { "hypercurve_all_features_unit_tests": "270 passed", "hypercurve_complete_all_features_suite": "pass", "hypercurve_focused_projective_unit_tests": "same/reversed complete and partial-range maps pass under STRICT and APPROXIMATE_512", "hypercurve_focused_curve_region_boolean": "26 tests; projective cubic regression passes under both policies", "hypercurve_no_default_focused_tests": "pass", "hypercurve_clippy_all_targets_all_features_deny_warnings": "pass", "hypercurve_clippy_all_targets_no_default_features_deny_warnings": "pass", "hypersolve_all_features": "167 unit, 2 readme, 131 residual-property, and 209 smoke tests pass", "hypersolve_no_default_features": "167 unit, 2 readme, 131 residual-property, and 209 smoke tests pass", "hypersolve_clippy_all_targets_all_features_deny_warnings": "pass", "formatting": "pass", "diff_check": "pass", "hypermesh_modified": false }, "remaining_boundaries": [ "shared components not reducible to lineage, degree alignment, endpoint-fixed projective control nets, conic/polynomial-graph maps, point incidence, or a certified injective coordinate still need exact bivariate branch evidence", "publish native conic and arc results compactly inside the authoritative arrangement", "reduce isolated single-operation topology construction overhead without restoring a second Boolean engine", "complete exact general offsets and solver-driven fillet/chamfer" ] }