docs: Dütsch protocol — worked cycle-index example, sparse sampling, driver unit tests

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/validation/duetsch_re100_kc5_protocol.md

@@ -101,6 +101,15 @@ Order (closed):
   mean cylinder position) versus x2, at the scored phases. Lab frame
   throughout; if any body-frame intermediate is used, position and velocity
   are both transformed.
+- Sampling cost: raw force and diagnostics counters are read every step
+  (small). Flags and velocity fields are read only at the steps inside the
+  three prescribed 1° phase bins (φ ∈ [180, 181), [210, 211), [330, 331),
+  T/360 steps each) of the cycles needed for settling and scoring, plus
+  sparse declared audits; never every step.
+- Point set: fixed x2/D sample points per station, identical on every grid
+  and declared before running; per point the interpolation weights are
+  recorded; the scored set is the common subset valid on all compared grids
+  at that phase, with its coverage recorded; point sets never change silently.
 - Interpolation: bilinear on cell centres using only cells that are fluid at
   that step (flags read back via `get_flags()`); weights renormalized over the
   fluid corners; a sample with no fluid corner, or inside the circle at that
@@ -124,6 +133,25 @@ force as denominator.
     three phases × four stations;
   - Morison `|dc_d| ≤ .02`, `|dc_i| ≤ .02`.
 - Rule: all metrics for N = 3 consecutive whole paper cycles → settled.
+
+Cycle indexing (worked example, binding). Paper cycle k spans
+`s/T in [0.25 + (k-1), 0.25 + k)`, i.e. φ0 → φ0; cycle 0 is the startup
+quarter `s/T < 0.25`. Pair p_k compares cycle k−1 with cycle k.
+
+- Discarded: cycles 0, 1, 2 (s/T < 2.25). Pairs are formed only between
+  cycles ≥ 3, so the first pair is p_4 (3 → 4).
+- Settling proof for a case: the earliest K_case such that p_{K-2}, p_{K-1},
+  p_K all pass (three consecutive pairs over cycles K−3 .. K). Earliest
+  possible: K_case = 6 (pairs 3→4, 4→5, 5→6).
+- Scored window (after the proof): cycles K+1, K+2, K+3 with
+  K = max over compared cases of K_case. The case must stay settled
+  throughout: pairs p_{K+1}, p_{K+2}, p_{K+3} must pass as well, otherwise
+  FAIL-CLOSED.
+- Cap: cycle k ends at s/T = 0.25 + k, so the window ends at s/T = K + 3.25
+  ≤ 12 ⇒ K ≤ 8. Allowed: K = 6 (window 7–9, ends 9.25 T), 7 (8–10,
+  10.25 T), 8 (9–11, 11.25 T). K_case > 8 for any case → FAIL-CLOSED.
+- Every case is run to the end of cycle K + 3 (proportionally more native
+  steps on finer grids).
 - Discard: the initial quarter cycle plus the first 2 full paper cycles
   (s/T < 2.25). Settling is searched from cycle 3; cap 12 periods from s = 0;
   unsettled → FAIL-CLOSED (no literature, cross-resolution or VIV statistic).
@@ -162,6 +190,15 @@ Superseded (earlier drafts): the velocity-jump start, guessed stations and
 phases, "C_M" for c_i, and the uncertainty wording; cycles 4–6, the 30-cycle
 cap and the earlier tolerance numbers.
 
+## 6a. Driver unit tests (CPU, before any run)
+
+- Phase/cycle arithmetic: s ↔ (k, φ), cycle boundaries, bin membership,
+  window/cap selection for K = 6, 7, 8, 9.
+- Solid-aware interpolation: all-fluid, partial-solid (renormalized weights),
+  no-fluid (MISSING) and inside-circle cases.
+- Interval-averaged Morison bases and the two-parameter fit on a synthetic
+  waveform with known c_d, c_i.
+
 ## 7. Order and scope
 
 Protocol review → one-shot Dütsch driver (analytic `set_body` + `run(1)`,