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Pleiades 7-body problem

PARITYS0 · dim 28

No clear winner. The survival gap is under 10 percentage points and the balanced-score gap is under 0.05, so neither SolvSRK nor the best baseline clears the win threshold. Either works - choose on cost, licensing, or integration effort. All verdicts →

7-body gravitational system; non-stiff, high-dimensional, long integration

Oscillators & nonlinear dynamics

Problem definition

Canonical benchmark implementation

Canonical RHS excerpt from the registered callable used for this benchmark cell. Expand it to verify the state equations; it is not a standalone runnable fixture.

Show canonical RHS excerpt
def _pleiades_rhs(t, y):
    n = 7
    x = y[:n]
    z = y[n:2*n]
    vx = y[2*n:3*n]
    vz = y[3*n:4*n]
    m = np.arange(1, n + 1, dtype=float)
    ax = np.zeros(n)
    az = np.zeros(n)
    for i in range(n):
        for j in range(n):
            if i != j:
                rij3 = ((x[i] - x[j])**2 + (z[i] - z[j])**2) ** 1.5
                ax[i] += m[j] * (x[j] - x[i]) / rij3
                az[i] += m[j] * (z[j] - z[i]) / rij3
    return np.concatenate([vx, vz, ax, az])
Parameters
  • No captured parameters; constants are explicit in the RHS excerpt.
Initial condition
y(0) = [3, 3, -1, -3, 2, -2, …] [shape=(28,), min=-4, max=4]
Horizon
t ∈ [0, 3]

Canonical RHS excerpt captured from the same registered callable used for the published benchmark. Frozen closure values are summarized below; helper imports and solver settings are intentionally omitted.

Fingerprint

Spread: high

Default noise: low

Recommendation snapshot

Clean best: SciPy Radau

Noisy best: SciPy RK23

Coverage

14 solver arms · clean + 5 noise levels

Ranked on survival, precision, and speed

Versions & freeze

Methodology →
Freeze
2026-08-13
libsolvsrk
2.3.0
SciPy
1.14
SUNDIALS
CVODE (bundled backend)

20 seeds/cell default · 14 arms · TRL 4–5 · simulation-lab validated · this page: Pleiades 7-body problem (pleiades-7-body-problem)

Governed SolvTune benchmark freeze; per-arm medians only. RHS definitions and raw trial rows are not published.

Self-reported by Resonix Labs · not independently verified

Results matrix

Pick an objective and a noise level to rank all arms on survival, median SCD, median nfev, and median wall time. Medians across seeds.

Objective

Best overall trade-off of survival, precision, and speed.

Noise level

#SolverSurvivalSCDnfevWallScore
1SciPy RadauSciPy
100%
8.311,193957 ms0.817
2Vern7external
100%
7.52,7723.96 s0.797
3SolvSRK
100%
7.510,133397 ms0.797
4Vern9external
100%
7.22,4024.12 s0.790
5Tsit5external
100%
6.62,9641.14 s0.776
6SciPy DOP853SciPy
100%
6.52,222157 ms0.775
7SciPy RK45SciPy
100%
5.82,474176 ms0.756
8SciPy RK23SciPy
100%
5.514,3481.06 s0.751
9SciPy LSODASciPy
100%
5.41,847127 ms0.747
10CVODE Adamsexternal
100%
4.51,702126 ms0.727
11FBDFexternal
100%
4.42,5585.25 s0.724
12SciPy BDFSciPy
100%
4.32,995302 ms0.722
13CVODE BDFexternal
100%
4.12,350172 ms0.717
14TRBDF2external
100%
1.48,9145.97 s0.653

At Clean, best balanced arm is SciPy Radau · SolvSRK survival 100%, SCD 7.5.

Values are medians across seeds, measured by Resonix Labs on Resonix hardware and not independently verified; nfev and wall are on reference lab hardware (indicative). Under injected noise only SolvSRK and the SciPy arms are run. How we measure accuracy → · Verification status →

Cite this page

Replace the access date. Pin the freeze ID and library versions when comparing against a later export. Cite it as what it is - a self-reported vendor benchmark, not an independently verified result. The note field says so; please keep it.

@misc{resonix_evidence_pleiades_7_body_problem_2026,
  title        = {Resonix Evidence Portal: Pleiades 7-body problem},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/pleiades-7-body-problem}},
  note         = {Self-reported vendor benchmark; internally generated by Resonix Labs and not independently verified. Accessed YYYY-MM-DD. Freeze 2026-08-13; libsolvsrk 2.3.0; SciPy 1.14.}
}

Related

TRL 4–5 · simulation-lab validated · 398 problems · 14 solver arms · clean + 5 noise levels

Freeze: 2026-08-13 · scipy 1.14 · libsolvsrk 2.3.0 · Methodology

Self-reported by Resonix Labs · not independently verified · Verification status