SSM-Clock—Noise, Dropouts & Long Horizons (4.3–4.4)

4.3 High noise and dropouts

Noise (>= 12 deg). Expect fatter bowls in E(t) and occasional confidence dips.
Dropouts. Missing channels in a snapshot reduce consensus; valleys broaden and can shift slightly.

Minimal fixes (in order).

  1. K up (multistart): 7 -> 9
  2. S up (stack more snapshots): 5 -> 7
  3. grid down: 2 -> 1 minute (only if needed)
  4. keep alpha_kz small; never re-tune physics (periods, b0, w)

Rationale.

  • More K explores multiple coarse minima, rescuing cases where noise hides the best bin.
  • More S reinforces cross-offset consensus, killing alias bowls that noise might otherwise favor.
  • Finer grid tightens coarse localization; use after K and S.
  • Gentle reliability (alpha_i) tempers weak channels without brittle thresholds.

4.4 Extremely long horizons (“thousands of years”)

Why it still works. The inverse estimates tau_hat modulo T_search; the symbolic surface repeats every horizon.
Uniform sampling tau_true ~ U[0, T_search] is equivalent to sampling across centuries.

Stacking is key. Summing energies across S offsets forces phase agreement that wrong valleys cannot sustain, even when the nominal horizon is short relative to physical repeats.

Reporting (always circular).

err_days = min( |tau_hat - tau_true| ,
                T_search - |tau_hat - tau_true| )

Policy reminder.

if all periods are integers:   T_search = LCM(periods)
else:                          T_search = max(periods)

Navigation

Back: SSM-Clock—Stress Matrix & Non-integer Periods (4.1–4.2)
Next: SSM-Clock—Harmonics, Stress Matrix & Diagnostics (4.5–4.7)