Generated by experiments/collect_results.py from the committed artifacts. Browsable at https://impact-adjoint.vercel.app/results. Every number below is read from an .npz or .npy in experiments/, not retyped, so this file cannot drift from what was measured.

Solver verification

quantity	value
observed order of accuracy (smooth arc vs analytic)	3.99
multi-bounce error vs symbolic closed form	1.35e-12
worst gradient-vs-FD agreement over 4 probes	8.13e-09
VJP marginal cost per parameter	15 us
affine cost model fit	R2 = 0.9981
symbolic closed-form oracle, worst Jacobian	7.1e-12
scipy reference oracle, worst primal	1.14e-10
scipy reference oracle, worst Jacobian vs FD	4.57e-09
energy drift at e=1, mu=0	4.63e-13
Tesseract check-gradients	0 failures / 150 checks on 3 endpoints

Warm per-call cost (dt 1e-3, t_final 2.0 s, four impacts)

params	apply	vector_jacobian_product	ratio
14	2.17 ms	7.24 ms	3.34x
77	2.84 ms	8.02 ms	2.82x
581	8.59 ms	15.8 ms	1.84x

Experiments

quantity	value
E3 grid-reset gradient (truth 0.09037774)	0
E3 interpolated-event relative error, coarse to fine	0.00209 to 5.6e-05
E3 saltation spread over the whole dt sweep	6.02e-14
E1 miss, start to final	1.12 m to 0.0269 m
E4 miss, slow and fast inlet	0.0216 m, 0.0303 m
E5 final objective, Adam / CMA-ES / Nelder-Mead	2.25e-07 / 0.00198 / 0.0186
E5 CMA tuning grid, median and best	0.00167 / 0.000165
E2b posterior e	0.6965 +/- 0.0071
E2b posterior mu	0.0955 +/- 0.0093
E2b divergences	0
E2b split r_hat, e and mu	1.01 / 1.01
E2b effective sample size of 2000 draws	344 / 330
E2b leapfrog steps, 2 chains (apply + VJP each)	23440
E2b warmup plus sampling wall time	23 min

Multi-seed benchmark and robustness

quantity	value
benchmark seeds, both methods tuned per seed	5
median final: Adam (eval accounting)	3.44e-07
median final: Adam (wall-clock accounting)	4.93e-08
median final: CMA-ES (tuned)	0.000315
median final: Nelder-Mead	0.99
CMA / Adam, paired per-seed median (eval, wall)	347x, 669x
CMA / Adam, ratio of medians (unpaired, for reference)	917x, 6.4e+03x
per-seed eval ratio span	11.5x to 1.4e+05x
held-out purity, point design	983/1000 (Wilson 97.29 to 98.94 %)
held-out purity, ensemble design	997/1000 (Wilson 99.12 to 99.90 %)
5th-percentile margin, point to ensemble	0.05 m to 0.494 m
worst-case margin, point to ensemble	-0.12 m to -0.353 m
decisive under jitter, point design	18/20 restitutions
decisive under jitter, ensemble design	20/20 restitutions

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