SSM-JTK – Data & Calibration — Kernel families & carriers (2.6)

Families (choose once per body)

• fixed-n — e.g., Moon, Jupiter, Saturn, Uranus, Neptune, Pluto. Uses a known sidereal rate: n = 360 / P_sid.
• free-n — e.g., Sun, Mercury, Venus, Mars. Learns a single slope n once and stores it in the manifest.

Carriers & constants (small, interpretable set)

• Sidereal period. P_sid (days); for fixed-n, n = 360 / P_sid.
• Synodic period. P_syn = 1 / | 1/P_sid − 1/365.2564 |.
• Synodic harmonics. w1 = 2*pi / P_syn, w2 = 2*w1, w3 = 3*w1 (tiny extras; gated).
• Slow sidereal wobble. wS = 2*pi / P_sid.
• Annual carrier (Earth). nE = 2*pi / 365.2564 (gated).

Design sets (parsimonious by default)

• BASE = { w1, w2, wS }
• CANDIDATE = BASE ∪ { nE } ∪ { w3 } ∪ { nE, w3 } (extras must pass the gate from §2.7)

Usage notes

• Keep the carrier pool minimal; admit extras only when they decisively improve event-aware loss and BIC (ΔBIC ≥ 6).
• Use the same t0 and time convention across experiments to avoid phase drift.
• For reporting, list the chosen family (fixed-n|free-n) and the final carrier set used by the selected model.

Manifest mapping (portable evaluator)

• fixed-n: store P_sid and harmonic coefficients; at runtime set n_deg_per_day = 360.0 / P_sid.
• free-n: store n_deg_per_day (learned) and harmonic coefficients.
  Evaluation one-liner (both families):
  L_hat_deg(t) = wrap360( a0_deg + n_deg_per_day*t + sum_k[ c_k*sin(w_k*t) + d_k*cos(w_k*t) ] ).

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