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Multi-language Kuramoto tier benchmark — CI vs local

Per-call P50 latency (microseconds) of every registered Kuramoto compute primitive across the Rust, Julia, and Python tiers, measured by scripts/bench_kuramoto_tiers.py. The canonical column is the fixed CI runner (Rust engine built from source); the local column is the GOTM workstation. Both are reproducible evidence, not published latency claims — hosted-runner CPU differs from the workstation. A — marks a tier not measured in that run (excluded subset or unavailable binding); see the per-environment artefacts under docs/benchmarks/tiers/ for the full percentile set and parity data.

Provenance

Field CI Local
CPU model AMD EPYC 7763 64-Core Processor 11th Gen Intel(R) Core(TM) i5-11600K @ 3.90GHz
Platform Linux-6.17.0-1018-azure-x86_64-with-glibc2.39 Linux-6.17.0-35-generic-x86_64-with-glibc2.39
Commit f9249f83c025d043bf84145ed1d6d79d6ec6fab2 352547b92161c3c28d4d6116b5ed3ecaea786a9d
Python 3.12.13 3.12.3
NumPy 2.2.6 2.2.6
Rust engine installed installed
juliacall 0.9.35 0.9.31
rustc rustc 1.96.0 (ac68faa20 2026-05-25) rustc 1.96.0 (ac68faa20 2026-05-25)

Runs

Environment Generated (UTC) Parameters
CI 2026-06-26T15:47:00Z tiers=[julia,python,rust] sizes=[8,32,128,512] warmup=2 repeats=5
Local 2026-06-24T23:56:12Z tiers=[python,rust] sizes=[8,32,128,512] warmup=2 repeats=5

Competitive Baseline Framing

This section is the Phase 5.5 claim boundary for the tier benchmark. It separates measured in-repository tier competition from unmeasured external package comparisons and production-latency claims.

Surface Current evidence Claim boundary
Internal tier competition CI measures 140 primitive-size rows; fastest counts: rust=108, julia=29, python=3. Supports dispatch-order and drift-detection decisions inside this package.
Python floor baseline Same-algorithm Python floor is measured in CI; fastest non-Python tiers show 3.90x median over 137 CI rows against that floor. This is not a claim of superiority over third-party Kuramoto, ODE, graph, or differentiable-solver packages.
External package baselines Not measured by this artefact. No external competitive claim is allowed until a separate harness records package names, versions, equations, tolerances, hardware, and raw artefacts.
Production latency Every committed tier artefact sets production_claim_allowed: false. No SLA, universal hardware, or customer deployment latency claim follows from this page.

Per-primitive P50 latency (µs)

Operation N Rust (CI) Rust (local) Julia (CI) Python (CI) Python (local) Fastest (CI) Parity (CI)
daido_mean_field_force 8 1.683 0.981 14.386 16.872 10.851 rust 1.11e-16
daido_mean_field_force 32 2.073 1.413 15.239 18.031 11.452 rust 8.33e-17
daido_mean_field_force 128 4.975 3.342 17.436 22.161 16.331 rust 4.16e-17
daido_mean_field_force 512 16.955 10.514 27.718 40.573 24.997 rust 5.55e-17
daido_mean_field_jacobian 8 3.657 1.505 14.912 25.624 15.579 rust 2.22e-16
daido_mean_field_jacobian 32 13.206 8.186 22.991 40.651 25.124 rust 1.67e-16
daido_mean_field_jacobian 128 189.100 178.621 148.591 257.792 224.765 julia 8.33e-17
daido_mean_field_jacobian 512 4549.686 3970.465 4132.213 4945.642 4079.830 julia 9.71e-17
daido_mode_phase 8 1.030 0.625 11.315 10.287 6.670 rust 1.11e-16
daido_mode_phase 32 1.767 0.836 11.669 10.530 7.043 rust 0.00e+00
daido_mode_phase 128 2.704 1.812 13.077 13.031 9.364 rust 1.11e-15
daido_mode_phase 512 8.555 5.699 17.450 21.738 14.019 rust 4.44e-16
daido_mode_phase_gradient 8 1.335 0.863 14.941 16.950 10.904 rust 2.22e-16
daido_mode_phase_gradient 32 2.103 1.420 14.965 18.386 11.674 rust 3.33e-16
daido_mode_phase_gradient 128 4.950 3.260 17.309 22.752 15.715 rust 9.99e-16
daido_mode_phase_gradient 512 16.719 11.560 28.753 41.224 27.368 rust 4.86e-17
daido_mode_phase_hessian 8 2.913 1.174 14.515 34.842 21.122 rust 3.33e-16
daido_mode_phase_hessian 32 5.390 2.268 17.523 40.331 25.917 rust 6.66e-16
daido_mode_phase_hessian 128 13.791 10.571 75.351 95.044 76.121 rust 4.00e-15
daido_mode_phase_hessian 512 153.538 157.005 2530.514 832.890 1072.336 rust 9.71e-17
daido_order_parameter 8 1.208 0.942 11.039 7.503 5.314 rust 0.00e+00
daido_order_parameter 32 1.259 0.929 11.315 8.176 5.639 rust 1.39e-17
daido_order_parameter 128 2.697 1.792 12.423 10.520 7.394 rust 0.00e+00
daido_order_parameter 512 8.706 5.699 16.513 20.333 14.110 rust 1.39e-17
daido_order_parameter_gradient 8 1.332 0.914 14.259 18.556 11.812 rust 2.78e-17
daido_order_parameter_gradient 32 2.117 1.410 15.075 19.693 12.213 rust 1.39e-17
daido_order_parameter_gradient 128 4.995 3.218 17.597 23.867 14.689 rust 1.50e-17
daido_order_parameter_gradient 512 16.604 10.595 28.056 41.926 35.873 rust 2.60e-18
daido_order_parameter_hessian 8 2.786 1.532 14.416 29.452 17.627 rust 5.55e-17
daido_order_parameter_hessian 32 4.420 1.731 17.101 33.572 21.021 rust 5.55e-17
daido_order_parameter_hessian 128 9.649 7.364 69.608 72.258 53.201 rust 4.86e-17
daido_order_parameter_hessian 512 117.453 170.593 2530.195 582.438 635.933 rust 5.20e-18
kuramoto_euler_trajectory 8 44.103 26.781 64.049 518.758 329.749 rust 4.44e-16
kuramoto_euler_trajectory 32 674.097 437.308 545.357 1325.482 864.166 julia 4.44e-16
kuramoto_euler_trajectory 128 11629.453 9203.602 8839.670 14046.759 10976.205 julia 1.33e-15
kuramoto_euler_trajectory 512 245285.731 204884.303 185975.370 272385.100 242535.154 julia 1.38e-14
kuramoto_euler_vjp 8 90.048 89.415 97.462 1237.979 1068.443 rust 4.44e-15
kuramoto_euler_vjp 32 1528.351 1119.381 1062.422 2982.642 2261.333 julia 9.95e-14
kuramoto_euler_vjp 128 28012.724 23078.208 19304.252 30590.731 28149.560 julia 1.17e-12
kuramoto_euler_vjp 512 563958.844 489273.842 445186.589 567717.732 569460.991 julia 4.80e-10
kuramoto_interaction_energy 8 1.941 1.315 17.478 8.087 6.936 rust 4.44e-16
kuramoto_interaction_energy 32 11.606 7.028 24.424 19.747 12.082 rust 3.44e-15
kuramoto_interaction_energy 128 169.783 158.591 138.626 208.441 164.070 julia 3.55e-15
kuramoto_interaction_energy 512 3621.024 3114.691 2700.310 4028.653 3521.759 julia 6.34e-12
kuramoto_interaction_energy_gradient 8 3.933 2.017 20.232 10.631 7.428 rust 5.55e-17
kuramoto_interaction_energy_gradient 32 11.961 9.263 28.356 24.207 16.715 rust 8.88e-16
kuramoto_interaction_energy_gradient 128 170.532 115.183 150.760 232.399 171.820 julia 8.88e-15
kuramoto_interaction_energy_gradient 512 3739.369 3504.444 2808.568 5031.270 4133.745 julia 3.02e-14
kuramoto_interaction_energy_hessian 8 4.162 1.631 21.259 13.141 8.298 rust 2.22e-16
kuramoto_interaction_energy_hessian 32 14.629 8.720 29.538 28.821 16.748 rust 8.88e-16
kuramoto_interaction_energy_hessian 128 228.605 172.773 171.623 269.153 221.272 julia 5.33e-15
kuramoto_interaction_energy_hessian 512 4932.920 4182.478 3341.814 5355.621 5058.333 julia 2.13e-14
kuramoto_rk4_trajectory 8 166.080 96.755 160.209 2288.617 1852.538 julia 1.39e-17
kuramoto_rk4_trajectory 32 2639.882 1621.924 1989.028 5468.826 3292.183 julia 8.88e-16
kuramoto_rk4_trajectory 128 43863.286 35132.240 33117.973 53739.508 45412.649 julia 2.00e-15
kuramoto_rk4_trajectory 512 990456.318 841726.505 775927.352 1089860.615 1072889.518 julia 4.31e-14
kuramoto_rk4_vjp 8 472.872 279.688 2174.882 6825.638 4760.977 rust 8.88e-16
kuramoto_rk4_vjp 32 7682.094 5590.547 27383.004 16080.444 11174.701 rust 6.66e-16
kuramoto_rk4_vjp 128 140636.165 116512.887 424203.501 161272.117 143605.952 rust 5.86e-14
kuramoto_rk4_vjp 512 2860566.657 2544101.383 7219909.881 3037485.262 2957652.493 rust 4.19e-09
local_mean_phase 8 2.067 1.427 20.262 9.030 5.538 rust 4.44e-16
local_mean_phase 32 3.809 2.594 22.043 10.545 6.119 rust 4.44e-16
local_mean_phase 128 23.456 18.652 41.296 18.674 13.889 python 5.33e-15
local_mean_phase 512 276.424 264.788 297.123 119.686 79.737 python 4.44e-15
local_mean_phase_jacobian 8 1.983 2.808 20.871 17.974 22.424 rust 4.44e-16
local_mean_phase_jacobian 32 4.112 5.272 23.511 23.671 30.011 rust 2.11e-15
local_mean_phase_jacobian 128 29.633 32.179 76.960 77.797 67.555 rust 1.19e-14
local_mean_phase_jacobian 512 400.209 380.471 2892.268 822.568 1032.108 rust 3.77e-15
local_order_parameter 8 1.916 1.252 19.828 10.888 7.118 rust 0.00e+00
local_order_parameter 32 3.939 2.314 21.669 12.937 8.456 rust 5.55e-17
local_order_parameter 128 19.993 15.932 38.286 24.519 17.008 rust 8.33e-17
local_order_parameter 512 262.964 242.960 280.346 178.904 139.451 python 8.33e-17
local_order_parameter_jacobian 8 2.705 2.695 20.544 20.043 13.266 rust 1.11e-16
local_order_parameter_jacobian 32 4.306 3.043 25.435 26.722 17.244 rust 4.16e-17
local_order_parameter_jacobian 128 29.451 24.665 79.093 85.316 75.314 rust 9.23e-17
local_order_parameter_jacobian 512 407.359 408.834 2820.087 901.474 958.829 rust 2.22e-17
mean_field_force 8 1.245 0.891 14.641 15.551 10.119 rust 2.22e-16
mean_field_force 32 2.124 1.309 15.045 16.563 10.678 rust 5.55e-17
mean_field_force 128 4.552 2.699 17.555 20.950 15.281 rust 2.78e-17
mean_field_force 512 15.466 9.222 27.121 38.469 22.291 rust 5.55e-17
mean_field_jacobian 8 3.209 1.450 14.946 23.129 16.256 rust 1.11e-16
mean_field_jacobian 32 12.372 7.223 22.322 37.532 22.538 rust 1.11e-16
mean_field_jacobian 128 173.826 130.693 135.594 232.760 168.044 julia 2.78e-17
mean_field_jacobian 512 3564.021 3140.961 3626.747 4195.702 3783.719 rust 5.55e-17
mean_phase 8 0.844 0.600 10.916 11.955 8.900 rust 3.12e-17
mean_phase 32 1.417 0.827 11.042 12.612 9.142 rust 0.00e+00
mean_phase 128 2.450 1.623 12.356 14.304 10.131 rust 8.33e-17
mean_phase 512 8.010 4.748 16.647 23.200 16.353 rust 4.44e-16
mean_phase_gradient 8 1.553 0.900 14.126 17.203 11.580 rust 1.11e-16
mean_phase_gradient 32 1.940 1.359 14.674 18.258 11.949 rust 1.11e-16
mean_phase_gradient 128 4.491 3.199 16.848 22.408 13.603 rust 1.11e-16
mean_phase_gradient 512 15.219 9.165 26.873 40.232 23.045 rust 1.73e-17
mean_phase_hessian 8 2.888 1.138 14.139 34.959 21.409 rust 1.11e-16
mean_phase_hessian 32 4.809 2.051 16.368 42.307 25.261 rust 8.33e-17
mean_phase_hessian 128 13.430 9.897 68.012 96.186 77.038 rust 1.25e-16
mean_phase_hessian 512 159.185 125.741 2492.929 812.134 702.525 rust 2.08e-17
networked_kuramoto_force 8 2.268 2.277 20.349 6.878 4.747 rust 1.11e-16
networked_kuramoto_force 32 11.746 7.134 27.132 18.197 11.116 rust 8.88e-16
networked_kuramoto_force 128 167.713 111.525 144.444 191.147 138.955 julia 5.33e-15
networked_kuramoto_force 512 3556.274 3090.903 2692.222 3993.759 3421.909 julia 2.49e-14
networked_kuramoto_jacobian 8 2.379 1.740 20.874 10.481 7.185 rust 2.22e-16
networked_kuramoto_jacobian 32 14.447 9.362 29.431 23.662 14.404 rust 8.88e-16
networked_kuramoto_jacobian 128 223.885 166.728 169.338 222.582 165.645 julia 5.33e-15
networked_kuramoto_jacobian 512 4950.946 3744.613 3208.239 4165.714 3832.477 julia 2.13e-14
order_parameter 8 0.801 0.561 10.937 7.600 5.513 rust 5.55e-17
order_parameter 32 1.129 0.748 10.950 7.994 6.816 rust 2.78e-17
order_parameter 128 2.380 1.516 12.149 10.543 7.403 rust 2.08e-17
order_parameter 512 7.574 5.537 15.804 19.754 13.615 rust 2.08e-17
order_parameter_gradient 8 1.261 0.909 14.396 16.758 10.763 rust 1.39e-17
order_parameter_gradient 32 1.947 1.328 14.908 17.950 11.471 rust 5.20e-18
order_parameter_gradient 128 4.496 3.089 17.238 22.043 15.022 rust 2.60e-18
order_parameter_gradient 512 15.229 12.786 27.357 39.601 24.471 rust 8.67e-19
order_parameter_hessian 8 1.428 0.996 13.642 25.641 16.731 rust 2.78e-17
order_parameter_hessian 32 4.348 1.613 16.226 32.065 19.861 rust 6.94e-18
order_parameter_hessian 128 9.292 6.733 114.014 61.868 50.051 rust 3.47e-18
order_parameter_hessian 512 112.524 124.214 2435.191 461.172 629.773 rust 8.67e-19
sakaguchi_force 8 3.380 1.581 21.395 13.913 5.981 rust 2.22e-16
sakaguchi_force 32 12.692 7.740 27.119 21.963 13.139 rust 8.88e-16
sakaguchi_force 128 193.576 129.766 151.912 208.158 139.121 julia 7.55e-15
sakaguchi_force 512 4402.744 3492.361 2932.638 4096.955 3534.242 julia 2.84e-14
sakaguchi_jacobian 8 4.006 2.607 20.509 11.447 8.620 rust 2.22e-16
sakaguchi_jacobian 32 14.584 9.416 30.179 24.912 16.777 rust 8.88e-16
sakaguchi_jacobian 128 221.988 176.519 167.316 216.512 170.657 julia 4.44e-15
sakaguchi_jacobian 512 4896.611 3813.868 3304.589 4080.802 3802.934 julia 2.58e-14
sakaguchi_mean_field_force 8 1.298 0.918 14.376 22.189 15.898 rust 1.11e-16
sakaguchi_mean_field_force 32 1.976 2.080 14.907 23.052 15.392 rust 6.25e-17
sakaguchi_mean_field_force 128 4.601 2.999 17.438 27.794 16.534 rust 2.78e-17
sakaguchi_mean_field_force 512 15.589 9.419 28.255 46.546 30.452 rust 4.16e-17
sakaguchi_mean_field_jacobian 8 3.521 1.491 14.702 26.712 18.378 rust 1.11e-16
sakaguchi_mean_field_jacobian 32 12.430 7.437 23.219 41.721 24.501 rust 1.11e-16
sakaguchi_mean_field_jacobian 128 173.776 135.615 140.861 234.290 174.131 julia 2.78e-17
sakaguchi_mean_field_jacobian 512 3458.771 3136.367 2880.023 4069.705 4158.522 julia 5.55e-17
triadic_mean_field_force 8 1.514 0.903 14.198 16.497 11.086 rust 8.33e-17
triadic_mean_field_force 32 2.308 1.303 15.217 17.624 11.665 rust 1.73e-17
triadic_mean_field_force 128 4.716 3.114 17.545 21.844 14.228 rust 2.17e-18
triadic_mean_field_force 512 16.035 10.290 27.313 39.899 28.797 rust 4.34e-18
triadic_mean_field_jacobian 8 3.064 2.705 15.463 34.184 32.938 rust 2.78e-16
triadic_mean_field_jacobian 32 17.772 18.336 30.631 58.581 37.492 rust 4.16e-17
triadic_mean_field_jacobian 128 270.705 258.240 277.521 516.023 442.142 rust 4.34e-18
triadic_mean_field_jacobian 512 6336.235 4600.139 6448.571 9538.710 8020.405 rust 7.81e-18