SSM-Clock—Harmonics, Stress Matrix & Diagnostics (4.5–4.7)

4.5 Optional shaped harmonics (keep a safety cap)

Shaped forward (small harmonics atop linear carriers).

phi_i(t) = wrap360( b0_i + w_i * t
                    + SUM_k [ c_{i,k} * sin(k*w_i' * t) + d_{i,k} * cos(k*w_i' * t) ] )

Speed–amplitude cap (avoid pathological wiggles).

A_speed_total_clock = SUM_i SUM_k [ |w_i'| * hypot(c_{i,k}, d_{i,k}) ]  <=  cap_clock

Policy.

  • Keep cap_clock small so the clock stays dominated by the linear carriers.
  • The inverse kernel E(t) is unchanged; only the forward phases are shaped.
  • Do not re-tune physics at runtime; harmonics are a frozen part of the manifest when used.

4.6 Stress matrix (quick guide)

Scenario                          Symptom                         Minimal fix (in order)
------------------------------------------------------------------------------------------------------------
Two channels (1,7)                Wrong valley at noise           Add 3rd cycle (e.g., 5) or S>=3 with 0.5 d
Non-integer periods present       Spurious repeats                T_search = max(periods) + stack S>=5
Noise ~ 6–12 deg                  PASS dips; P95 grows            K up -> S up -> grid down -> (optional) stride down
Channel dropouts                  Confidence dips; jitter         Keep stacking; small alpha_kz; diversify periods
Very long spans (centuries)       Concern about drift             Uniform tau sampling; report modulo T_search
Adding harmonics                  Overfit-like jitter             Enforce A_speed_total_clock <= cap_clock
Flat curvature bowl               conf ~ 0                        Add diversified cycle or raise S; check delta spacing

4.7 Diagnostic checklist (fast, ASCII-only)

  • D1. Confidence sanity. Log curvature-based conf; flat bowls should show conf ~ 0.
  • D2. Residuals at tau_hat. Print per-channel err_i(tau_hat); if one outlier dominates, apply gentle alpha_i (keep k_z small).
  • D3. Grid stress. Halve grid_step_min once; if results stabilize and PASS rises, keep the finer grid.
  • D4. K vs S trade. Start at K=7, S=5. If aliasing is suspected, raise S first; if noisy minima, raise K first.
  • D5. Period diversity. Prefer mixes like {1, 7, 5, 29.5306, 365.2422}; diversity beats over-tuning.
  • D6. One-wrap discipline. Wrap only inside angdiff; avoid double-wrap in forward terms.

Navigation

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