3.5 What “PASS” means (policy)
Definition (per seed). Convert circular time error to minutes and compare to a fixed gate:
err_days_mod = min( |tau_hat - tau_true| ,
T_search - |tau_hat - tau_true| )
err_min = 1440.0 * err_days_mod
PASS(seed) := ( err_min <= 28.8 ) # 28.8 min = 0.02 day
Definition (over a sweep). Require a high fraction of seeds to pass:
pass_rate = 100.0 * pass_count / seeds
Gate := ( pass_rate >= 95.0 )
v1.1 acceptance.
- Noise levels tested: 2 deg and 6 deg.
- Both meet PASS at the above gate with 200 seeds per noise point.
Why 28.8 minutes.
- A stable, interpretable envelope for “minutes-level” recognition.
- Leaves headroom for integration noise in real systems while staying strict enough for offline symbolic timing.
Why “thousands of years” is inherent.
- The inverse estimates
tau_hatmoduloT_search; the symbolic surface repeats every horizon. - Uniform sampling across
[0, T_search]is equivalent to sampling across very long ranges.
err_days_mod = min( |tau_hat - tau_true| ,
T_search - |tau_hat - tau_true| )
- Stacking across offsets forces consensus that wrong valleys cannot sustain, preserving accuracy even when nominal spans are long.
Practical notes.
- When PASS under tough noise is marginal, adjust in this order:
K up -> S up -> grid down -> coarse_stride down -> refine bracket/steps up. - Report mean error and P95 alongside
pass_ratefor auditors.
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