longTauGnssCoupling: coast-cap + graded-taper primitives (unit layer)

[bobvan]

Summary

The unit layer for longTauGnssCoupling — four pure policy functions in discipline.py, not yet wired into DisciplineScheduler. Reviewing the API shape + math now (both the engine wiring and Charlie's closedLoopServoSim will consume these signatures).

The bug they target: the scheduler's τ = √(2·T/D) budgets only the deterministic drift. A quiet DO (D≈0) gets τ→max_interval (120 s), but its stochastic phase wander keeps growing over the coast — the tau~64–256 s TDEV hump in the 2026-05-29 overnight runs (PiFace 6.4 ns @ 64 s, MadHat 3.6 ns @ 256 s), exactly where GNSS is at its best.

function	what it does
coast_cap_from_tdev	invert a power-law freerun TDEV → largest τ with k·TDEV(τ) ≤ budget. DO-class: ~138 s for an 85 ps OCXO, <1 s for a 1.17 ns TCXO. slope≤0 ⇒ no constraint.
coast_cap_from_p22	largest int τ with k·√(P22(τ)) ≤ budget; P22 from a caller closure over the filter's predict-only growth.
normalized_convergence	map √(P22)/σ_total → [0,1] — the single derived signal every policy reads (disciplineModeFsm reframe).
graded_interval	geometric taper replacing the binary 1 if converging else interval latch (and its 1→120 s actuation cliff). Continuous + monotone ⇒ cannot chatter.

Connections to the rest of the redesign

• Depends on qFromCharPerActuator (Main): the √(P22) cap is only honest in the characterized small-Q regime — with an inflated Q it's spuriously tight. Per Main's take, qFromCharPerActuator lands first; this layer is reviewable independently but wires after it.
• Main's growth-law correction: coast P-growth is dominated by the frequency random-walk integrated into phase (Var ≈ q_f·τ³/3, σ ∝ τ^1.5), not the phase term. coast_cap_from_p22 is agnostic (callable); a test pins the cubic-variance shape.
• graded_interval is the continuous converging→tracking transition (Bob's emergent-not-latched preference); it's also a candidate fix for pifaceShortTauGlitches candidate (a), the coast-end actuation cliff.

Test plan

• 28 unit tests (TDEV inversion incl. OCXO/TCXO/RW-FM, P22 cap incl. freq-RW cubic + exact boundary, normalized ramp, taper monotonicity + no-cliff, composition)
• Wire into compute_adaptive_interval (behind params, default-off) after qFromCharPerActuator
• Closed-loop A/B in closedLoopServoSim: confirm the tau~64–256 s hump drops

🤖 Generated with Claude Code

[bobvan]

REVIEW (charlie) — LGTM. Math verified on all four primitives + 28 tests pass; full review on the dayplan (longTauGnssCoupling thread, 2026-05-28). Two minor non-blocking nits: (1) normalized_convergence reads inverted vs its name (returns 1.0 when least-converged — naming-honesty); (2) coast_cap_from_p22 scans O(max_tau) closure calls (negligible at 1Hz). Design is sim-friendly — I'll consume coast_cap_from_p22 in closedLoopServoSim's coast gate once qFromCharPerActuator lands honest Q[3,3]. Ship the unit layer.

[bobvan]

Superseded by #86 (longTau stack squashed into one PR per Bob, 2026-05-29). The primitives (Charlie-approved here) + scheduler wiring + engine wiring all live in #86. Thanks @charlie for the review — the normalized_distance_to_lock rename + the 4-primitive math all carried into #86 unchanged.