research: Dütsch --dump-fields capture (research-only; default path unchanged)

At the first step of each scored phase bin in the declared cycles, write a
near-body crop (±8D × ±6D, float32 ux, uy, rho + fluid mask), an 8x
fluid-weighted downsample of the whole domain, the same-step force and the
analytic centre; at every bin read, append fluid-mean rho/ux/uy and crop,
inlet- and outlet-strip means to trend.npy. Fail closed if the crop leaves the
domain or clips the swept body. Without --dump-fields nothing changes.

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

docs/validation/duetsch_re100_kc5_protocol.md

@@ -0,0 +1,242 @@
+# Prescribed in-line oscillation: Dütsch Re 100 / KC 5 — PROTOCOL (review draft)
+
+Production under test: `claude/moving-bodies-s3a` at `653fd997` (unchanged).
+Primary source: Dütsch, Durst, Becker & Lienhart, J. Fluid Mech. 360, 249–271
+(1998), doi:10.1017/S002211209800860X. Source facts below were verified from
+the paper (Slack C0C78UFKGRM/1793335557.460509, TRON 1793356317–1793356724,
+page numbers given). Everything marked ENGINEERING is our a-priori choice,
+fixed before any benchmark result; it is not a paper uncertainty.
+
+## 0. Source facts (with provenance)
+
+- Motion (p.251): `x_c = -A sin(2 pi f t)`; paper phase phi = 0 is the mean
+  position moving left at `-U_max`. KC = 5 gives `A/D = 5/(2 pi) = .7957747`.
+- Start (p.254): the computation starts a quarter cycle before phi = 0, at
+  `x = +A` with zero velocity (phi = -90°).
+- Experiment (pp.252, 254–256): D = 10 mm, L = .65 m, tank 1.2 × .7 × .7 m,
+  rho = 998.2 kg/m³, mu = 1.00818 mPa·s, Re = 100, KC = 5; LDA with 1° phase
+  bins and 200 samples per node and degree; no quantified experimental error
+  recovered.
+- Profiles (Fig. 8, p.260): LAB-FIXED stations x1 = -6, 0, 6, 12 mm, i.e.
+  x/D = -.6, 0, .6, 1.2, at phi = 180°, 210°, 330°; u1 and u2 versus x2.
+- Original numerics (§2): cylinder-fixed accelerated frame (`x_i = x~_i +
+  x_i,s`, outer velocity `-u_c`, inertial source `-rho du_c/dt`), O-grid outer
+  diameter 120 D, illustrated 192 circumferential nodes, 720 steps/cycle; tank
+  influence neglected.
+- Force fit (verified): force ON THE BODY per unit span
+  `F1 = -0.5 rho D c_d xdot|xdot| - (pi/4) rho D² c_i xddot` with `x = -A sin phi`;
+  normalized by `0.5 rho D U_max²`: `c_d cos phi |cos phi| - (pi² c_i / KC) sin phi`.
+  `c_i` is the ADDED-MASS coefficient; total inertia `c_m = c_i + 1` is a
+  different convention and is not used.
+- Table 1 computed Morison coefficients (c_d, c_i) for 96 / 192 / 384 perimeter
+  nodes at dt/T = 1/720: (2.15, 1.42), (2.10, 1.45), (2.09, 1.45). These are
+  fitted computed coefficients, not a measured force and not an error bar. The
+  paper states the coarse direct force is closer to the finest direct force
+  than the Morison fit, but gives no waveform-error norm.
+
+## 1. Kinematics, time levels and phase bookkeeping
+
+- Our run is in the LAB frame: the circle moves, the fluid is initially at rest
+  (rho = 1, u = 0); no fictitious inertial source is added. Lab-fixed profile
+  stations are compared directly (no frame transform needed).
+- Geometry reference: the circle's base centre is the INITIAL position, the
+  right turning point `x_mean + A`; the declared offset box is x in [-2A, 0],
+  y = 0. The body is never teleported: offset 0 at s = 0.
+- Elapsed time s = n dt from the start. Analytic position relative to the mean
+  `x(s) = A cos(2 pi s / T)`, velocity `u(s) = -U_max sin(2 pi s / T)`; paper
+  phase `phi = (360 s / T - 90) mod 360`.
+- Step n moves from s_n to s_{n+1}: target offset `x(s_{n+1}) - A`; wall
+  velocity = the single-step interval average `(x(s_{n+1}) - x(s_n)) / dt`
+  (analytic, supplied, not differenced from stored offsets). The per-step
+  force of `run(1)` / `read_force(normalize=True)` is attributed to that same
+  interval.
+- Paper cycle k = 1, 2, ... spans `s in [T/4 + (k-1) T, T/4 + k T)`; the
+  initial quarter cycle (s < T/4) is cycle 0 and never scored. Every logged
+  sample carries (k, phi). Example: phi = 330° of cycle 1 is at s = 7T/6.
+- T is chosen as a multiple of 360 native steps, so phi = 180°, 210°, 330° fall
+  exactly on step boundaries and 1° bins hold whole steps.
+
+## 2. Resolution ladder (uniform grid, fixed Mach), ENGINEERING
+
+| D (cells) | T (steps) | U_max = 5 D / T | nu_lat = U_max D / 100 | tau (3 nu + .5) |
+|---|---|---|---|---|
+| 20 | 2,520 | .039683 | .0079365 | .5238 |
+| 40 | 5,040 | .039683 | .015873 | .5476 |
+| 80 | 10,080 | .039683 | .031746 | .5952 |
+
+- MRT collision. Mach fixed (Ma ≈ .0687); a separate Mach check at D = 40
+  with T = 10,080 (U_max halved, tau .5238) is labelled MACH and not part of the
+  ladder.
+- Per-step displacement ≤ U_max ≈ .04 cells (bound .5).
+
+## 3. Domain and boundaries (finite-domain reproduction), ENGINEERING
+
+The paper's 120 D O-grid is not reproduced; our rectangular box is a
+reproduction choice. The native dense channel (zero-velocity inlet,
+pressure-NEQ outlet, bounce-back y walls) is a finite-domain approximation,
+not infinite still fluid. The G4 x-periodic / y-slip override is a separately
+labelled sensitivity family and never mixed into the primary ladder. The
+runner owner confirms the zero-velocity inlet is supported as configured
+before any run.
+
+Order (closed):
+1. Smoke + ledger at D = 40, native BC, 40 D × 40 D (finite box).
+2. Domain sensitivity before any literature statement: same BC, D = 40,
+   L ∈ {20 D, 40 D, 60 D}; record the change in Fx waveform, c_d, c_i and the
+   scored profiles.
+3. Optional labelled BC sensitivity: one x-periodic / y-slip case at D = 40,
+   40 D; reported as a delta against native only.
+4. Only after step 2 passes: the D = 20 / 40 / 80 ladder on the chosen BC and
+   domain.
+
+Domain criteria (a-priori, ENGINEERING; separate from the Table 1 bands): the
+reference is 60 D at D = 40; 20 D and 40 D are compared with it on the common
+window (same cycle indices) and the common valid point set:
+- `RMS(Fx_L - Fx_60D) / F_ref ≤ .01` over the window (per-step waveforms);
+- `|c_d,L - c_d,60D| ≤ .02` and `|c_i,L - c_i,60D| ≤ .02` (window fits);
+- `max(|u_L - u_60D|, |v_L - v_60D|)` over common points `/ U_max ≤ .02`.
+The chosen domain is the smallest of {20 D, 40 D} passing all three; if
+neither passes, the domain verdict is FAIL and the ladder is not run.
+- Memory/runtime: measured by a smoke run before each new size; measurements
+  inform scheduling only, never tolerances.
+
+## 4. Observables (raw, per step, preserved)
+
+- `obs` Fx, Fy (CME) and all `MovingTables.DIAG` columns per step: CME,
+  CME + Wen and CME + cover − uncover reported separately; crossings, eq_only,
+  no_donor (no_donor must stay 0).
+- Velocity u1, u2 on lab-fixed lines x/D = -.6, 0, .6, 1.2 (relative to the
+  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
+  step, is MISSING and logged, never set to zero. One-degree bins keep valid
+  fluid weights. The numerical average need not mimic the 200 LDA samples.
+
+## 5. Periodic-regime gate (every case, before any statistic), ENGINEERING
+
+Ledger rows, same schema for every case: dx, dt (in D and T units); U_max, nu,
+Re, KC (lattice and nondimensional); T (native steps, nondimensional);
+duration (native steps, s/T, paper cycles); discard; accepted window; cycle
+ledger; verdict PASS or FAIL-CLOSED.
+
+Scales: `F_ref = 0.5 rho U_max² D`, `U_ref = U_max`; never a near-zero mean
+force as denominator.
+
+- Settling metrics, cycle k−1 → k, phase-aligned by step within the cycle
+  (error budget: one fifth of the tightest comparison band of the same
+  observable, so residual drift cannot obscure a domain or resolution pass):
+  - waveform `RMS(dFx) / F_ref ≤ .002`;
+  - `|d mean|`, `|d RMS|`, `|d peak|` of Fx, each `/ F_ref ≤ .002`;
+  - scored profiles (fluid-only) `|du| / U_max`, `|dv| / U_max ≤ .004` at the
+    three phases × four stations;
+  - Morison `|dc_d| ≤ .004`, `|dc_i| ≤ .004`.
+- Conservative comparison: every domain and cross-resolution criterion is
+  applied to `|difference| + drift_a + drift_b`, where drift is the largest
+  pair metric of that case inside the scored window.
+- These constants (protocol.py SETTLE, DOMAIN, CROSS) are frozen before any
+  physical result; no post-result loosening.
+- 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: three consecutive pairs all pass; K_case = the
+  first cycle AFTER the last of those pairs. Earliest possible: pairs 3→4,
+  4→5, 5→6 pass ⇒ K_case = 7.
+- Common window: K = max over compared cases of K_case; every case scores the
+  same three complete cycles K, K+1, K+2 and must stay settled continuously:
+  every pair p_j for j = its own K_case .. K+2 must pass (including the wait
+  between its local settle and the common K), otherwise that case is
+  FAIL-CLOSED.
+- Cap: cycle k ends at s/T = k + 0.25, so the last admissible scored cycle is
+  11 (ends 11.25 T) and K ≤ 9. Examples: K = 7 → cycles 7–9 (ends 9.25 T);
+  K = 9 → cycles 9–11 (ends 11.25 T); any K_case > 9 → FAIL-CLOSED.
+- Run length: cases run sequentially; each runs to the end of cycle 11
+  (11.25 T: 28,350 / 56,700 / 113,400 steps for D = 20 / 40 / 80; the 12 T
+  cap is 30,240 / 60,480 / 120,960) and keeps its scalar and profile data, then
+  the common K is chosen. An unscorable partial cycle 12 is not run.
+- Profiles: an empty common valid point set is FAIL-CLOSED; coverage, missing
+  points, bin time weights (equal per step) and the original fluid corner
+  weight sums are reported.
+- The earlier G4 timing check (100 coarse vs 400 diffusive-fine steps) was a
+  matched short transient, not periodic evidence.
+
+## 6. Metrics and per-observable criteria (ENGINEERING, not paper uncertainty)
+
+Three criteria stay separate; the G4 same-grid 2% target is not reused.
+
+- Morison fit: least squares of the normalized per-step force over the
+  accepted window against the two basis functions, each averaged over its
+  single step interval, fixed paper phase, no free phase shift; c_d and
+  added-mass c_i per force candidate.
+- Cross-resolution: every scored observable's error against its reference must
+  decrease monotonically D20 → D40 → D80 (necessary, not sufficient).
+- Against Table 1 (computed fit, not measured force): at D ≥ 40,
+  `|c_d - 2.09| ≤ .15` and `|c_i - 1.45| ≤ .15`, and monotone.
+- Force waveform against its own Morison reconstruction: residual reported
+  only, no pass/fail (the paper reports fit error above its coarse numerical
+  error and gives no percentage).
+- Fig. 8 LDA profiles: QUALITATIVE ONLY. The original figure could not be
+  accessed or rendered; no digitized ordinates and no measurement uncertainty
+  exist. After a digitization with figure number, tool and uncertainty note:
+  `RMS(|du|, |dv|) / U_max ≤ .15` at D ≥ 40 and monotone; LDA error stays
+  UNQUANTIFIED and is stated with every comparison.
+- Fy sanity (not literature): `|mean Fy| / F_ref ≤ .05` in the accepted window.
+- No force candidate is selected for an RHS by these results; each is
+  reported.
+
+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.
+
+## 6b. Amendment: duration-only diagnostic (declared before the run)
+
+- Background: the D40 domain stage (20 D / 40 D / 60 D, 11.25 T each) failed
+  settling in every box (no window). That result stands.
+- One declared diagnostic: D = 40, 60 D box, from rest, through cycle 31
+  (157,500 steps = 31.25 T). Physics, settling tolerances, bands and
+  production unchanged; three proof pairs plus a continuously settled
+  K..K+2 with K ≤ 29.
+- Invocation: `run.py --D 40 --box 60 --cycles 31` then
+  `analyze.py --horizon 31`; the JSON records `horizon` and `horizon_mode`.
+  Without `--horizon` the analyzer is the original cap-11 scoring.
+- Failure at 31.25 T: report and stop; no automatic extension, matrix, D80
+  or VIV. A pass shows only that this box settles with time; it is not a
+  domain or literature pass.
+- The phase-locked high-frequency force component (residual of the mean
+  waveform after its Morison reconstruction, above 20/T) is reported per case
+  as unqualified; it needs separate qualification before any Morison or
+  literature statement.
+
+## 6a. Driver unit tests (CPU, before any run)
+
+- Phase/cycle arithmetic: s ↔ (k, φ), cycle boundaries, bin membership,
+  window/cap selection for K = 7, 8, 9, 10.
+- 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)`,
+cycle ledger, lab-fixed fluid-only station sampler, two-basis Morison fit; no
+reusable runner until the first smoke shows shared helpers pay off; no
+production change) → smoke (memory/runtime) → domain sensitivity →
+ladder → physical-validation verdict → only then single-cylinder VIV. No AMR,
+no pinball, no manuscript work.

research/duetsch_re100_kc5/analyze.py

@@ -0,0 +1,224 @@
+"""Ledger, settling, common window and Morison fits for Dütsch cases (numpy only).
+
+    python analyze.py CASE_DIR [CASE_DIR ...]   # cases of one comparison
+"""
+from __future__ import annotations
+
+import json
+import math
+import os
+import sys
+
+import numpy as np
+
+import protocol as p
+
+
+def load(path):
+    with open(os.path.join(path, "case.json")) as fh:
+        case = json.load(fh)
+    raw = np.load(os.path.join(path, "raw.npz"))
+    case.update(force=raw["force"], diag=raw["diag"], samples=raw["samples"], path=path)
+    return case
+
+
+def cycle_slices(case):
+    """{k: slice of step indices m whose interval [m, m+1] lies in paper cycle k}."""
+    T, q = case["T"], case["T"] // 4
+    return {k: slice(q + (k - 1) * T, q + k * T)
+            for k in range(1, case["cycles"] + 1) if q + k * T <= len(case["force"])}
+
+
+def coarse_wave(case, k, r=1):
+    """Normalized per-step Fx of cycle k, averaged over r native steps per sample."""
+    f = case["force"][cycle_slices(case)[k], 0] / case["F_ref"]
+    return f.reshape(-1, r).mean(axis=1)
+
+
+def profiles(case, k):
+    """{(phase, station, x2): (u, v)} of cycle k, time-averaged over the bin steps
+    (equal weights per step) from valid samples only."""
+    s = case["samples"]
+    acc = {}
+    for _, _, ph, xs, x2, u, v, _ in s[s[:, 1] == k]:
+        if not (math.isnan(u) or math.isnan(v)):
+            acc.setdefault((ph, xs, x2), []).append((u, v))
+    return {key: tuple(np.mean(vals, axis=0)) for key, vals in acc.items()}
+
+
+def coverage(case, k):
+    s = case["samples"]
+    rows = s[s[:, 1] == k]
+    missing = int(np.isnan(rows[:, 5]).sum())
+    return dict(samples=len(rows), missing=missing, bin_steps=len(set(rows[:, 0])),
+                min_fluid_weight=float(np.nanmin(np.where(rows[:, 7] > 0, rows[:, 7], np.nan)))
+                if len(rows) else math.nan)
+
+
+def common_points(dicts):
+    keys = set(dicts[0])
+    for d in dicts[1:]:
+        keys &= set(d)
+    return sorted(keys)
+
+
+def candidates(case):
+    """Per-step Fx of each reported force candidate (none is selected as an RHS)."""
+    d = case["diag"]
+    return {"cme": d[:, 0], "cme_wen": d[:, 0] + d[:, 2], "cme_node": d[:, 0] + d[:, 6] - d[:, 9]}
+
+
+def cycle_morison(case, ks, fx=None):
+    T = case["T"]
+    fx = case["force"][:, 0] if fx is None else fx
+    idx = np.concatenate([np.arange(len(fx))[cycle_slices(case)[k]] for k in ks])
+    b = np.array([p.interval_bases(int(m), T) for m in idx])
+    return p.morison_fit(fx[idx] / case["F_ref"], b[:, 0], b[:, 1])
+
+
+def pair_metrics(case, k):
+    a, b = coarse_wave(case, k - 1), coarse_wave(case, k)
+    pa, pb = profiles(case, k - 1), profiles(case, k)
+    common = common_points([pa, pb])  # empty set -> inf -> pair fails (FAIL-CLOSED)
+    prof = max((max(abs(pa[c][0] - pb[c][0]), abs(pa[c][1] - pb[c][1])) for c in common),
+               default=math.inf) / case["u_max"]
+    (cd0, ci0), (cd1, ci1) = cycle_morison(case, [k - 1]), cycle_morison(case, [k])
+    m = dict(wave=float(np.sqrt(np.mean((b - a) ** 2))),
+             scalar=float(max(abs(b.mean() - a.mean()), abs(np.sqrt(np.mean(b * b)) - np.sqrt(np.mean(a * a))),
+                              abs(np.abs(b).max() - np.abs(a).max()))),
+             profile=float(prof), morison=float(max(abs(cd1 - cd0), abs(ci1 - ci0))),
+             profile_points=len(common))
+    m["pass"] = all(m[key] <= tol for key, tol in p.SETTLE.items())
+    return m
+
+
+def hf_component(case, ks):
+    """Unqualified phase-locked high-frequency force component (reported, not checked):
+    mean CME waveform over cycles ks minus its two-basis Morison reconstruction,
+    split at 20/T; cycle differencing does not remove it."""
+    T = case["T"]
+    if not ks:
+        return dict(label="unqualified phase-locked HF force component, not checked", cycles=[])
+    mean = np.mean([coarse_wave(case, k) for k in ks], axis=0)
+    c_d, c_i = cycle_morison(case, ks)
+    q = T // 4
+    b = np.array([p.interval_bases(q + m, T) for m in range(T)])
+    resid = mean - (c_d * b[:, 0] - (np.pi ** 2 * c_i / p.KC) * b[:, 1])
+    spec = np.fft.rfft(resid)
+    high = spec.copy()
+    high[:21] = 0.0
+    energy = one_sided_energy(spec, T)
+    return dict(label="unqualified phase-locked HF force component, not checked",
+                cycles=list(ks), hf_rms_over_F_ref=float(np.sqrt(np.mean(np.fft.irfft(high, T) ** 2))),
+                hf_energy_fraction=float(energy[21:].sum() / max(energy.sum(), 1e-300)),
+                top_harmonics=[int(j) for j in np.argsort(energy[21:])[::-1][:5] + 21])
+
+
+def one_sided_energy(spec, n):
+    """Parseval-consistent energy per rfft bin: interior bins count twice, DC and
+    (for even n) Nyquist once."""
+    w = np.full(len(spec), 2.0)
+    w[0] = 1.0
+    if n % 2 == 0:
+        w[-1] = 1.0
+    return w * np.abs(spec) ** 2
+
+
+def ledger(case, horizon=p.LAST_SCORED):
+    ks = [k for k in sorted(cycle_slices(case)) if k <= horizon]
+    pairs = {k: pair_metrics(case, k) for k in ks if k - 1 > p.DISCARD}
+    return pairs, p.settled_start({k: v["pass"] for k, v in pairs.items()})
+
+
+def main(argv):
+    """argv: CASE_DIR ... [--reference CASE_DIR]; the reference defaults to the
+    largest D (resolution ladder); domain runs name the 60 D case explicitly."""
+    ref_path = None
+    if "--reference" in argv:
+        i = argv.index("--reference")
+        ref_path, argv = argv[i + 1], argv[:i] + argv[i + 2:]
+    horizon, explicit = p.LAST_SCORED, "--horizon" in argv  # default: original scoring
+    if explicit:
+        i = argv.index("--horizon")
+        horizon, argv = int(argv[i + 1]), argv[:i] + argv[i + 2:]
+    paths = argv if ref_path is None or ref_path in argv else argv + [ref_path]
+    cases = [load(path) for path in paths]
+    for c in cases if explicit else ():  # complete cycles 1..N; never pad or shift
+        if c["cycles"] < horizon or len(c["force"]) < round((0.25 + horizon) * c["T"]):
+            raise SystemExit(f"{c['path']}: run does not contain complete cycles 1..{horizon}")
+    ledgers = [ledger(c, horizon) for c in cases]
+    window = p.common_window([k for _, k in ledgers],
+                             [{k: v["pass"] for k, v in pairs.items()} for pairs, _ in ledgers],
+                             last_scored=horizon)
+    report = dict(window=window, horizon=horizon, cases=[],
+                  horizon_mode="default-cap" if horizon == p.LAST_SCORED else
+                  "extended duration diagnostic (declared amendment, D40/60D only)")
+    for case, (pairs, k_case) in zip(cases, ledgers):
+        limit = round((0.25 + horizon) * case["T"])  # events inside the horizon only
+        entry = {key: case[key] for key in ("path", "D", "T", "box", "n", "u_max", "nu", "tau", "A",
+                                            "steps", "cycles", "F_ref")}
+        entry.update(duration_T=case["steps"] / case["T"], K_case=k_case, pairs=pairs,
+                     coverage={k: coverage(case, k) for k in sorted(cycle_slices(case))
+                               if p.DISCARD < k <= horizon},
+                     no_donor=float(case["diag"][:limit, 13].sum()),
+                     eq_only=float(case["diag"][:limit, 12].sum()),
+                     hf_component=hf_component(case, window or tuple(
+                         [k for k in sorted(cycle_slices(case)) if p.DISCARD < k <= horizon][-3:])))
+        if window:  # residual drift inside the scored window (pairs K..K+2)
+            entry["window_drift"] = {key: max(pairs[k][key] for k in window)
+                                     for key in ("wave", "profile", "morison")}
+            entry["morison_obs"] = cycle_morison(case, window)
+            entry["morison"] = {name: cycle_morison(case, window, fx)
+                                for name, fx in candidates(case).items()}
+            entry["fy_mean"] = float(np.mean(np.concatenate(
+                [case["force"][cycle_slices(case)[k], 1] for k in window])) / case["F_ref"])
+        report["cases"].append(entry)
+    if window and len(cases) > 1:  # cross-resolution waveform against the finest case
+        fine = (next(c for c in cases if c["path"] == ref_path) if ref_path
+                else max(cases, key=lambda c: c["D"]))
+        report["reference"] = fine["path"]
+        ref = np.concatenate([coarse_wave(fine, k) for k in window])
+        for case, entry in zip(cases, report["cases"]):
+            r = fine["T"] // case["T"]  # 1 for equal-D domain runs
+            ref_c = ref.reshape(-1, r).mean(axis=1)
+            own = np.concatenate([coarse_wave(case, k) for k in window])
+            entry["wave_rms_vs_finest"] = float(np.sqrt(np.mean((own - ref_c) ** 2)))
+        for k in window:  # profiles on the common valid point set of all compared cases
+            per_case = [profiles(c, k) for c in cases]
+            keys = common_points(per_case)
+            report.setdefault("common_profile_points", {})[k] = len(keys)
+            if not keys:
+                report["verdict"] = "FAIL-CLOSED: empty common profile set"
+                continue
+            fine_p = per_case[cases.index(fine)]
+            for case, entry, prof in zip(cases, report["cases"], per_case):
+                d = max(max(abs(prof[key][0] - fine_p[key][0]), abs(prof[key][1] - fine_p[key][1]))
+                        for key in keys) / case["u_max"]
+                entry.setdefault("profile_max_vs_finest", {})[k] = float(d)
+        ref_entry = report["cases"][cases.index(fine)]
+        for entry in report["cases"]:  # conservative: difference + both drifts
+            if entry is ref_entry:
+                continue
+            drift = {key: entry["window_drift"][key] + ref_entry["window_drift"][key]
+                     for key in ("wave", "profile", "morison")}
+            dm = max(abs(entry["morison"]["cme"][0] - ref_entry["morison"]["cme"][0]),
+                     abs(entry["morison"]["cme"][1] - ref_entry["morison"]["cme"][1]))
+            entry["conservative"] = dict(
+                wave=entry["wave_rms_vs_finest"] + drift["wave"],
+                profile=max(entry.get("profile_max_vs_finest", {}).values(), default=math.inf)
+                + drift["profile"],
+                morison_cme=dm + drift["morison"])
+            bands = p.DOMAIN if ref_path else p.CROSS  # domain runs name the 60 D reference
+            c = entry["conservative"]
+            entry["pass_scope"] = (
+                ("wave+profile+morison_cme" if "morison" in bands else "wave+profile")
+                + ": conservative (|diff| + both window drifts) on the obs/CME Fx waveform and "
+                "simulation-to-simulation profiles; CME+Wen and CME+node reported, not checked; "
+                "no Fig. 8 / literature verdict")
+            entry["pass"] = (c["wave"] <= bands["wave"] and c["profile"] <= bands["profile"]
+                             and ("morison" not in bands or c["morison_cme"] <= bands["morison"]))
+    print(json.dumps(report, indent=1, default=float))
+
+
+if __name__ == "__main__":
+    main(sys.argv[1:])

research/duetsch_re100_kc5/capture.py

@@ -0,0 +1,52 @@
+"""Research-only field capture helpers for the Dütsch driver (numpy only).
+
+Snapshots are taken at the first step of the scored phase bins in declared
+cycles: a near-body crop at full resolution and a fluid-weighted block-mean
+downsample of the whole domain; plus scalar trends at every bin read.
+"""
+from __future__ import annotations
+
+import numpy as np
+
+CROP_X, CROP_Y, DOWN = 8.0, 6.0, 8      # crop half-widths in D; downsample factor
+STRIP = 2.0                             # inlet/outlet strip width in D
+
+
+def crop_box(xm, ym, D, n, body_extent):
+    """Inclusive integer crop (x0, x1, y0, y1); fail closed if it leaves the domain
+    interior or does not contain the body's swept extent (x_lo, x_hi, y_lo, y_hi)."""
+    x0, x1 = int(round(xm - CROP_X * D)), int(round(xm + CROP_X * D))
+    y0, y1 = int(round(ym - CROP_Y * D)), int(round(ym + CROP_Y * D))
+    if x0 < 1 or y0 < 1 or x1 > n - 2 or y1 > n - 2:
+        raise ValueError("capture crop leaves the domain interior")
+    bx0, bx1, by0, by1 = body_extent
+    if not (x0 <= bx0 and bx1 <= x1 and y0 <= by0 and by1 <= y1):
+        raise ValueError("capture crop clips the body's swept extent")
+    return x0, x1, y0, y1
+
+
+def downsample(field, fluid, f=DOWN):
+    """Fluid-weighted f x f block means; NaN where a block has no fluid cell."""
+    ny, nx = field.shape
+    h, w = ny // f, nx // f
+    v = np.where(fluid, field, 0.0)[:h * f, :w * f].reshape(h, f, w, f).sum(axis=(1, 3))
+    c = fluid[:h * f, :w * f].reshape(h, f, w, f).sum(axis=(1, 3))
+    with np.errstate(invalid="ignore", divide="ignore"):
+        return np.where(c > 0, v / np.maximum(c, 1), np.nan).astype(np.float32)
+
+
+def fluid_mean(field, fluid, xs=slice(None), ys=slice(None)):
+    m = fluid[ys, xs]
+    return float(field[ys, xs][m].mean()) if m.any() else float("nan")
+
+
+def trend_row(s, k, ph, rho, ux, uy, fluid, D, n, crop):
+    """(s, cycle, phase, <rho>, <ux>, <uy>, <rho>_crop, inlet <rho>, <ux>, outlet <rho>, <ux>)."""
+    w = max(1, int(round(STRIP * D)))
+    x0, x1, y0, y1 = crop
+    cx, cy = slice(x0, x1 + 1), slice(y0, y1 + 1)
+    inlet, outlet, inner = slice(1, 1 + w), slice(n - 1 - w, n - 1), slice(1, n - 1)
+    return (s, k, ph, fluid_mean(rho, fluid), fluid_mean(ux, fluid), fluid_mean(uy, fluid),
+            fluid_mean(rho, fluid, cx, cy),
+            fluid_mean(rho, fluid, inlet, inner), fluid_mean(ux, fluid, inlet, inner),
+            fluid_mean(rho, fluid, outlet, inner), fluid_mean(ux, fluid, outlet, inner))

research/duetsch_re100_kc5/protocol.py

@@ -0,0 +1,129 @@
+"""Pure arithmetic of the Dütsch Re 100 / KC 5 protocol (numpy only, no CUDA).
+
+docs/validation/duetsch_re100_kc5_protocol.md is the contract: elapsed time s
+in native steps from the right turning point, paper phase
+phi = (360 s / T - 90) mod 360, paper cycle k >= 1 spans
+s/T in [0.25 + (k-1), 0.25 + k); cycle 0 is the startup quarter.
+"""
+from __future__ import annotations
+
+import math
+
+import numpy as np
+
+KC, RE = 5.0, 100.0
+STATIONS = (-0.6, 0.0, 0.6, 1.2)          # lab-fixed x/D from the mean position
+PHASES = (180.0, 210.0, 330.0)            # degrees; bins [p, p + 1)
+X2 = tuple(np.round(np.arange(-1.5, 1.5001, 0.05), 10))  # declared x2/D points
+DISCARD, LAST_SCORED, N_PAIRS = 2, 11, 3   # cycles 0..2 discarded, cap 12 T
+# A-priori bands. Settling is one fifth of the tightest comparison band of the
+# same observable, and comparisons add both cases' residual window drift
+# (conservative: |difference| + drift_a + drift_b <= band).
+DOMAIN = dict(wave=.01, morison=.02, profile=.02)  # vs the 60 D reference at D = 40
+CROSS = dict(wave=.02, profile=.02)                # D40 vs D80
+SETTLE = dict(wave=.002, scalar=.002, profile=.004, morison=.004)
+
+
+def amplitude(D):
+    return KC * D / (2.0 * math.pi)
+
+
+def position(s, T, A):
+    """Centre position relative to the mean: x = A cos(2 pi s / T), evaluated from the
+    native step modulo T so every cycle repeats the same geometry bit for bit."""
+    return A * math.cos(2.0 * math.pi * (int(s) % T) / T)
+
+
+def phase(s, T):
+    """Paper phase in degrees from the native step modulo T (the unwrapped cycle
+    index is kept separately by ``cycle``)."""
+    return (360.0 * (int(s) % T) / T - 90.0) % 360.0
+
+
+def cycle(s, T):
+    return 0 if s < 0.25 * T else int(math.floor(s / T - 0.25)) + 1
+
+
+def bin_phase(s, T):
+    """Scored phase whose 1-degree bin [p, p + 1) contains time s, else None."""
+    phi = phase(s, T)
+    for p in PHASES:
+        if p <= phi < p + 1.0:
+            return p
+    return None
+
+
+def interval_bases(n, T, points=16):
+    """Single-step interval averages over [n, n + 1] of cos phi |cos phi| and sin phi
+    (phi in radians = 2 pi s / T - pi / 2), Gauss-Legendre quadrature."""
+    x, w = np.polynomial.legendre.leggauss(points)
+    s = int(n) % T + 0.5 * (x + 1.0)  # periodic: identical bases in every cycle
+    phi = 2.0 * np.pi * s / T - 0.5 * np.pi
+    c = np.cos(phi)
+    return 0.5 * float(np.sum(w * c * np.abs(c))), 0.5 * float(np.sum(w * np.sin(phi)))
+
+
+def morison_fit(f_norm, b1, b2):
+    """Least squares of f_norm = c_d b1 - (pi^2 c_i / KC) b2 (paper phase, no shift)."""
+    a = np.column_stack([b1, -(math.pi ** 2 / KC) * np.asarray(b2)])
+    (c_d, c_i), *_ = np.linalg.lstsq(a, np.asarray(f_norm), rcond=None)
+    return float(c_d), float(c_i)
+
+
+def inside_circle(x, y, centre, radius):
+    return (x - centre[0]) ** 2 + (y - centre[1]) ** 2 < radius * radius
+
+
+def sample(field, fluid, x, y, centre, radius):
+    """Profile sample: MISSING if the exact point is inside the body (checked before
+    any corner interpolation), else ``bilinear_fluid``."""
+    if inside_circle(x, y, centre, radius):
+        return None, (), 0.0
+    return bilinear_fluid(field, fluid, x, y)
+
+
+def bilinear_fluid(field, fluid, x, y):
+    """Bilinear value at (x, y) in cell coordinates from fluid cells only.
+
+    Returns (value, ((ix, iy, weight), ...), fluid_weight_sum) with weights
+    renormalized over the fluid corners and the original sum of their bilinear
+    weights, or (None, (), 0.0) when no corner is fluid (MISSING, never zero).
+    """
+    x0, y0 = int(math.floor(x)), int(math.floor(y))
+    fx, fy = x - x0, y - y0
+    corners = ((x0, y0, (1 - fx) * (1 - fy)), (x0 + 1, y0, fx * (1 - fy)),
+               (x0, y0 + 1, (1 - fx) * fy), (x0 + 1, y0 + 1, fx * fy))
+    used = [(i, j, w) for i, j, w in corners if w > 0.0 and fluid[j, i]]
+    total = sum(w for _, _, w in used)
+    if total == 0.0:
+        return None, (), 0.0
+    used = tuple((i, j, w / total) for i, j, w in used)
+    return float(sum(w * field[j, i] for i, j, w in used)), used, float(total)
+
+
+def settled_start(pairs_pass):
+    """K_case from {k: pass of pair (k-1 -> k)}: first cycle after three consecutive
+    passing pairs among cycles > DISCARD, or None."""
+    run = 0
+    for k in sorted(pairs_pass):
+        if k - 1 <= DISCARD:
+            continue
+        run = run + 1 if pairs_pass[k] else 0
+        if run == N_PAIRS:
+            return k + 1
+    return None
+
+
+def common_window(k_cases, pairs_pass_by_case, last_scored=LAST_SCORED):
+    """Common scored cycles K..K+2 with K = max K_case, or None (FAIL-CLOSED) when a
+    case never settled, K + 2 exceeds the cap, or a case fails any pair p_j for
+    j = its own K_case .. K + 2 (continuous settling, including the wait for K)."""
+    if any(k is None for k in k_cases):
+        return None
+    K = max(k_cases)
+    if K + 2 > last_scored:
+        return None
+    for k_case, pairs in zip(k_cases, pairs_pass_by_case):
+        if not all(pairs.get(j, False) for j in range(k_case, K + 3)):
+            return None
+    return K, K + 1, K + 2

research/duetsch_re100_kc5/run.py

@@ -0,0 +1,133 @@
+"""One-shot Dütsch Re 100 / KC 5 prescribed in-line oscillation driver.
+
+Protocol: docs/validation/duetsch_re100_kc5_protocol.md. Native dense channel
+(zero-velocity inlet, pressure-NEQ outlet, bounce-back y walls), MRT, lab frame.
+Writes raw per-step force/diagnostics and phase-bin profile samples to --out
+(outside the checkout); analysis is in analyze.py. No production change.
+
+    python run.py --D 40 --box 40 --cycles 11 --out /path/outside/checkout
+"""
+from __future__ import annotations
+
+import argparse
+import json
+import math
+import os
+import tempfile
+
+import numpy as np
+
+import protocol as p
+
+
+TEMPLATE = os.path.join(os.path.dirname(os.path.abspath(__file__)), "..", "..", "src",
+                        "CelerisLab", "configs", "config_lbm.json")
+
+
+def config(D, box, T):
+    """Shipped config_lbm.json (full parser schema) with only the case fields
+    overridden: grid, still fluid (velocity 0), nu from Re, MRT, uniform inlet
+    profile, bounce-back y walls. Inlet scheme and outlet mode stay the
+    template's (zou_he_local, neq_extrap) and are recorded in case.json."""
+    u = p.KC * D / T
+    n = int(round(box * D))
+    with open(TEMPLATE) as fh:
+        cfg = json.load(fh)
+    cfg["grid"].update(lattice_model="D2Q9", nx=n, ny=n, nz=1)
+    cfg["physics"].update(data_type="FP32", viscosity=u * D / p.RE, velocity=0.0, rho=1.0)
+    cfg["method"].update(collision="MRT", streaming="double_buffer", store_precision="FP32",
+                         ddf_shifting=False, y_wall_bc="bounce_back")
+    cfg["method"]["les"]["enabled"] = False
+    cfg["method"]["inlet"]["profile"] = "uniform"
+    return cfg, u, n
+
+
+def main():
+    ap = argparse.ArgumentParser()
+    ap.add_argument("--D", type=int, required=True)
+    ap.add_argument("--box", type=float, default=40.0, help="box side in D")
+    ap.add_argument("--T", type=int, default=None, help="period in steps (multiple of 360)")
+    ap.add_argument("--cycles", type=int, default=p.LAST_SCORED, help="run to the end of this cycle")
+    ap.add_argument("--out", required=True)
+    ap.add_argument("--dump-fields", default="",
+                    help="research capture: comma-separated paper cycles, e.g. 11,21,30,31")
+    args = ap.parse_args()
+    D, T = args.D, args.T or 126 * args.D
+    if T % 360:
+        raise SystemExit("T must be a multiple of 360 steps")
+    if os.path.realpath(args.out).startswith(os.path.realpath(os.path.join(os.path.dirname(__file__), "..", ".."))):
+        raise SystemExit("--out must be outside the checkout")
+    cfg, u_max, n = config(D, args.box, T)
+    A, R = p.amplitude(D), 0.5 * D
+    xm = ym = 0.5 * (n - 1)
+    os.makedirs(args.out, exist_ok=True)
+
+    from CelerisLab.body.motion import Translation
+    from CelerisLab.simulation import Simulation
+    with tempfile.NamedTemporaryFile("w", suffix=".json", delete=False) as fh:
+        json.dump(cfg, fh)
+    sim = Simulation(fh.name)
+    try:
+        body = sim.add_body("circle", (xm + A, ym), R,
+                            translation=Translation((-2.0 * A, 0.0, 0.0, 0.0), 1.01 * u_max))
+        sim.initialize()
+        dump = {int(c) for c in args.dump_fields.split(",") if c}
+        if dump:
+            import capture
+            if max(dump) > args.cycles or min(dump) <= p.DISCARD:
+                raise SystemExit("--dump-fields cycles must lie in the scored range of this run")
+            crop = capture.crop_box(xm, ym, D, n, (xm - A - R, xm + A + R, ym - R, ym + R))
+            trend = []
+        steps = int(round((0.25 + args.cycles) * T))
+        force = np.zeros((steps, 2)); diag = []; samples = []
+        for m in range(steps):
+            x0, x1 = p.position(m, T, A), p.position(m + 1, T, A)
+            sim.set_body(body, offset=(max(x1 - A, -2.0 * A), 0.0), vx=x1 - x0)
+            sim.run(1)
+            force[m] = sim.read_force(body)[:2]
+            diag.append(sim.moving_diagnostics()[0])
+            s = m + 1  # state after the step
+            ph = p.bin_phase(s, T)
+            if ph is not None and p.cycle(s, T) > p.DISCARD:
+                fields = sim.get_macroscopic()
+                fluid = (sim.get_flags().reshape(n, n) & 1) != 0
+                ux, uy = (np.asarray(fields[k]).reshape(n, n) for k in ("ux", "uy"))
+                if dump:  # research capture only; the default path is unchanged
+                    rho = np.asarray(fields["rho"]).reshape(n, n)
+                    trend.append(capture.trend_row(s, p.cycle(s, T), ph, rho, ux, uy, fluid, D, n, crop))
+                    if p.cycle(s, T) in dump and p.phase(s, T) == ph:  # first step of the bin
+                        x0c, x1c, y0c, y1c = crop
+                        cy_, cx_ = slice(y0c, y1c + 1), slice(x0c, x1c + 1)
+                        np.savez_compressed(
+                            os.path.join(args.out, f"fields_c{p.cycle(s, T)}_p{int(ph)}.npz"),
+                            s=s, cycle=p.cycle(s, T), phase=ph, crop=np.asarray(crop),
+                            force=force[m], centre=np.asarray((xm + p.position(s, T, A), ym)),
+                            ux=ux[cy_, cx_].astype(np.float32), uy=uy[cy_, cx_].astype(np.float32),
+                            rho=rho[cy_, cx_].astype(np.float32), fluid=fluid[cy_, cx_].astype(np.uint8),
+                            down_ux=capture.downsample(ux, fluid), down_uy=capture.downsample(uy, fluid),
+                            down_rho=capture.downsample(rho, fluid))
+                centre = (xm + p.position(s, T, A), ym)  # analytic centre after the step
+                for xs in p.STATIONS:
+                    for x2 in p.X2:
+                        x, y = xm + xs * D, ym + x2 * D
+                        u, wu, wsum = p.sample(ux, fluid, x, y, centre, R)
+                        v, _, _ = p.sample(uy, fluid, x, y, centre, R)
+                        samples.append((s, p.cycle(s, T), ph, xs, x2,
+                                        math.nan if u is None else u, math.nan if v is None else v,
+                                        wsum, json.dumps(wu)))
+        if dump:
+            np.save(os.path.join(args.out, "trend.npy"), np.asarray(trend, float))
+        np.savez(os.path.join(args.out, "raw.npz"), force=force, diag=np.asarray(diag),
+                 samples=np.asarray([r[:8] for r in samples], float))
+        with open(os.path.join(args.out, "case.json"), "w") as fh:
+            json.dump(dict(D=D, T=T, box=args.box, n=n, u_max=u_max, nu=cfg["physics"]["viscosity"],
+                           tau=3 * cfg["physics"]["viscosity"] + 0.5, A=A, steps=steps,
+                           cycles=args.cycles, F_ref=0.5 * u_max ** 2 * D,
+                           inlet=cfg["method"]["inlet"], outlet=cfg["method"]["outlet"],
+                           weights=[r[8] for r in samples]), fh)
+    finally:
+        sim.close()
+
+
+if __name__ == "__main__":
+    main()

tests/unit/test_duetsch_protocol.py

@@ -0,0 +1,191 @@
+"""CPU tests of the Dütsch protocol arithmetic (docs/validation/duetsch_re100_kc5_protocol.md §6a)."""
+import importlib.util
+import math
+from pathlib import Path
+
+import numpy as np
+import pytest
+
+_spec = importlib.util.spec_from_file_location(
+    "duetsch_protocol", Path(__file__).resolve().parents[2] / "research/duetsch_re100_kc5/protocol.py")
+p = importlib.util.module_from_spec(_spec)
+_spec.loader.exec_module(p)
+
+T = 2520
+
+
+def test_phase_and_cycle_bookkeeping():
+    assert p.phase(0, T) == 270.0 and p.cycle(0, T) == 0          # +A, at rest, phi = -90
+    assert p.phase(T // 4, T) == 0.0 and p.cycle(T // 4, T) == 1  # mean position, u = -U_max
+    assert p.position(0, T, 1.0) == 1.0
+    assert p.cycle(T // 4 - 1, T) == 0 and p.cycle(T // 4 + T - 1, T) == 1
+    assert p.cycle(T // 4 + T, T) == 2
+    assert p.phase(T // 6, T) == pytest.approx(330.0) and p.cycle(T // 6, T) == 0  # startup quarter
+    assert p.phase(7 * T // 6, T) == pytest.approx(330.0) and p.cycle(7 * T // 6, T) == 1
+    for ph, frac in ((180.0, .75), (210.0, 5 / 6)):
+        s = round(frac * T) + T
+        assert p.phase(s, T) == pytest.approx(ph) and p.bin_phase(s, T) == ph
+    assert p.bin_phase(round(.75 * T) + T - 1, T) is None
+    assert sum(p.bin_phase(s, T) == 180.0 for s in range(T, 2 * T)) == T // 360
+
+
+def test_settling_and_common_window():
+    passes = {k: True for k in range(3, 12)}
+    assert p.settled_start(passes) == 7                          # pairs 3->4, 4->5, 5->6
+    late = {**passes, 5: False}
+    assert p.settled_start(late) == 9                            # pairs 6->7, 7->8, 8->9
+    assert p.common_window([7, 9], [passes, passes]) == (9, 10, 11)
+    assert p.common_window([7, 10], [passes, passes]) is None    # K + 2 = 12 beyond the cap
+    assert p.common_window([7, None], [passes, passes]) is None
+    assert p.common_window([7, 7], [passes, {**passes, 8: False}]) is None  # must stay settled
+    # a case settled early must keep passing while waiting for the common K
+    assert p.common_window([7, 9], [{**passes, 8: False}, passes]) is None
+    long = {k: True for k in range(3, 32)}
+    assert p.common_window([10], [long]) is None                 # default cap 11
+    assert p.common_window([29], [long], last_scored=31) == (29, 30, 31)
+    assert p.common_window([30], [long], last_scored=31) is None
+
+
+def test_solid_aware_bilinear():
+    field = np.arange(16.0).reshape(4, 4)
+    fluid = np.ones((4, 4), bool)
+    value, used, total = p.bilinear_fluid(field, fluid, 1.25, 1.5)
+    assert total == pytest.approx(1.0) and value == pytest.approx(0.75 * 0.5 * (5 + 9) + 0.25 * 0.5 * (6 + 10))
+    fluid[1, 1] = False                                           # one solid corner
+    value, used, total = p.bilinear_fluid(field, fluid, 1.25, 1.5)
+    assert total == pytest.approx(1.0 - 0.75 * 0.5)
+    assert all(not (i == 1 and j == 1) for i, j, _ in used)
+    assert sum(w for *_, w in used) == pytest.approx(1.0)
+    fluid[:] = False
+    assert p.bilinear_fluid(field, fluid, 1.25, 1.5) == (None, (), 0.0)
+
+
+def test_interval_bases_and_morison_fit_recover_known_coefficients():
+    b = np.array([p.interval_bases(n, T) for n in range(T // 4, T // 4 + 3 * T)])
+    phi = 2 * np.pi * (np.arange(T // 4, T // 4 + 3 * T) + .5) / T - np.pi / 2
+    assert np.allclose(b[:, 1], np.sin(phi), atol=1e-5)          # midpoint ~ interval mean
+    f = 2.09 * b[:, 0] - (math.pi ** 2 * 1.45 / p.KC) * b[:, 1]
+    assert p.morison_fit(f, b[:, 0], b[:, 1]) == pytest.approx((2.09, 1.45), abs=1e-9)
+
+
+def test_geometry_repeats_exactly_across_cycles():
+    A = p.amplitude(20)
+    for m in (0, 1, T // 4, T // 2 - 1, 7 * T // 12):
+        for c in (1, 5, 11):
+            assert p.position(m + c * T, T, A) == p.position(m, T, A)
+            assert p.phase(m + c * T, T) == p.phase(m, T)
+            v0 = p.position(m + 1, T, A) - p.position(m, T, A)
+            assert p.position(m + 1 + c * T, T, A) - p.position(m + c * T, T, A) == v0
+    assert p.cycle(T // 4 + 5 * T, T) == 6  # unwrapped index stays separate
+    assert p.interval_bases(123 + 7 * T, T) == p.interval_bases(123, T)
+
+
+def test_exact_point_inside_body_is_missing_even_with_fluid_corners():
+    field = np.zeros((6, 6))
+    fluid = np.ones((6, 6), bool)
+    fluid[3, 3] = False                         # only one corner solid
+    centre, radius = (3.0, 3.0), 0.3
+    value, used, total = p.sample(field, fluid, 3.2, 3.1, centre, radius)   # inside the circle
+    assert value is None and used == () and total == 0.0
+    value, used, total = p.sample(field, fluid, 3.35, 3.0, centre, radius)  # just outside
+    assert value is not None and total > 0.0
+
+
+def test_generated_config_passes_the_real_loader(tmp_path):
+    import json
+    import sys
+    sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "research/duetsch_re100_kc5"))
+    try:
+        import run
+    finally:
+        sys.path.pop(0)
+    from CelerisLab.config import load_lbm_config
+    cfg_dict, u_max, n = run.config(20, 10.0, 2520)
+    path = tmp_path / "config_lbm.json"
+    path.write_text(json.dumps(cfg_dict))
+    cfg = load_lbm_config(str(path))
+    assert (cfg.nx, cfg.ny) == (n, n) == (200, 200)
+    assert cfg.collision == "MRT" and cfg.streaming == "double_buffer" and not cfg.ddf_shifting
+    assert cfg.velocity == 0.0 and cfg.viscosity == pytest.approx(u_max * 20 / 100)
+    assert cfg.y_wall_bc == "bounce_back"
+
+
+def _analyze():
+    import sys
+    sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "research/duetsch_re100_kc5"))
+    try:
+        import analyze
+    finally:
+        sys.path.pop(0)
+    return analyze
+
+
+def test_hf_energy_is_parseval_weighted():
+    a = _analyze()
+    n = 360
+    t = np.arange(n)
+    x = 1.0 + np.cos(2 * np.pi * 5 * t / n) + 2.0 * np.cos(2 * np.pi * 30 * t / n) + 0.5 * np.cos(np.pi * t)
+    e = a.one_sided_energy(np.fft.rfft(x), n) / n
+    assert e.sum() == pytest.approx(np.sum(x ** 2))               # Parseval
+    expected = (2.0 ** 2 / 2 + 0.5 ** 2) / np.mean(x ** 2)       # bins >= 21 (30 and Nyquist)
+    assert e[21:].sum() / e.sum() == pytest.approx(expected)
+
+
+def test_horizon_excludes_future_coverage_and_events(monkeypatch):
+    a = _analyze()
+    T, horizon = 360, 4
+    steps = round((0.25 + 6) * T)                                 # cycles 1..6 recorded
+    diag = np.zeros((steps, 15))
+    diag[round((0.25 + horizon) * T):, 13] = 1.0                  # synthetic future no_donor
+    rows = [(s, p.cycle(s, T), 180.0, 0.0, 0.0, 0.1, 0.0, 1.0) for s in range(steps)
+            if p.bin_phase(s, T) is not None and p.cycle(s, T) > p.DISCARD]
+    case = dict(path="c", D=20, T=T, box=10, n=200, u_max=.04, nu=.008, tau=.524, A=1.0,
+                steps=steps, cycles=6, F_ref=1.0, force=np.zeros((steps, 2)), diag=diag,
+                samples=np.asarray(rows, float))
+    monkeypatch.setattr(a, "load", lambda path: case)
+    out = []
+    monkeypatch.setattr("builtins.print", lambda text: out.append(text))
+    a.main(["c", "--horizon", str(horizon)])
+    import json
+    entry = json.loads(out[0])["cases"][0]
+    assert sorted(int(k) for k in entry["coverage"]) == [3, 4]   # nothing from cycles 5, 6
+    assert entry["no_donor"] == 0.0
+
+
+
+def _capture():
+    spec = importlib.util.spec_from_file_location(
+        "duetsch_capture", Path(__file__).resolve().parents[2] / "research/duetsch_re100_kc5/capture.py")
+    mod = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(mod)
+    return mod
+
+
+def test_capture_crop_downsample_and_trends():
+    c = _capture()
+    n, D = 2400, 40
+    xm = ym = 0.5 * (n - 1)
+    A, R = p.amplitude(D), 20.0
+    box = c.crop_box(xm, ym, D, n, (xm - A - R, xm + A + R, ym - R, ym + R))
+    assert box == (880, 1520, 960, 1440) and box[1] - box[0] + 1 == 641 and box[3] - box[2] + 1 == 481
+    with pytest.raises(ValueError):
+        c.crop_box(xm, ym, D, 600, (0, 1, 0, 1))                    # leaves the domain
+    with pytest.raises(ValueError):
+        c.crop_box(xm, ym, D, n, (xm - 9 * D, xm, ym, ym))           # clips the swept body
+    field = np.arange(64.0).reshape(8, 8)
+    fluid = np.ones((8, 8), bool)
+    fluid[:4, :4] = False
+    down = c.downsample(field, fluid, 4)
+    assert np.isnan(down[0, 0]) and down[1, 1] == field[4:, 4:].mean()
+    rho = np.ones((n, n)); rho[:, 1:81] = 1.01
+    row = c.trend_row(10, 3, 180.0, rho, np.zeros((n, n)), np.zeros((n, n)),
+                      np.ones((n, n), bool), D, n, box)
+    assert row[7] == pytest.approx(1.01) and row[9] == pytest.approx(1.0)
+
+
+def test_dump_steps_are_the_first_step_of_each_bin():
+    T = 5040
+    for k in (11, 21, 30, 31):
+        starts = [s for s in range(T // 4 + (k - 1) * T, T // 4 + k * T)
+                  if p.bin_phase(s, T) is not None and p.phase(s, T) == p.bin_phase(s, T)]
+        assert len(starts) == 3 and all(p.cycle(s, T) == k for s in starts)