Context. The kernel stays fixed; difficulty is handled by strengthening the inverse (stack + multistart) and by diversifying cycles. Below are failure modes, symptoms, and the smallest safe fixes that keep everything ephemeris-free and ASCII-only.
4.1 Two-cycle aliasing (why 2 channels are risky)
What happens. With 2 commensurate or near-commensurate periods (e.g., 1 and 7 days), E(t) has strong repeating valleys. One noisy snapshot can lock onto a wrong valley.
Symptom.
- Residuals may look good, but
tau_hatis wrong modulo the true horizon. - Confidence can be lower (flat bowl).
Minimal fixes.
- Add a third diversified period (e.g., 5-day or lunar).
- Or keep 2 channels but stack
S >= 3snapshots with a non-integer spacing (e.g.,0.5day).
4.2 Non-integer periods (exact repeats are astronomical)
Context. If any period is non-integer (e.g., 29.5306), the joint repeat (true LCM) is huge.
Policy (deterministic).
if all periods are integers: T_search = LCM(periods)
else: T_search = max(periods)
Why it works. Using max(periods) gives a tight, sufficient window; stacking across offsets eliminates spurious valleys that would otherwise appear over very long repeats.
When to increase S. If PASS dips near the gate at higher noise, raise S (e.g., 5 -> 7) before touching other knobs.
Reporting (always circular).
err_days = min( |tau_hat - tau_true| ,
T_search - |tau_hat - tau_true| )
Navigation
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