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diff --git a/Tests/SpectroEELSTests/Fixtures/eels16-pins.json b/Tests/SpectroEELSTests/Fixtures/eels16-pins.json
new file mode 100644
index 0000000..0fba27a
--- /dev/null
+++ b/Tests/SpectroEELSTests/Fixtures/eels16-pins.json
@@ -0,0 +1,6675 @@
+{
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+     true,
+     true,
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+     true,
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+     true,
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+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
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+     true,
+     true,
+     true,
+     true,
+     true,
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+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
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+     true,
+     true,
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+     true,
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+     true,
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+     true,
+     true,
+     true,
+     true,
+     true,
+     true,
+     true
+    ]
+   }
+  },
+  "shift1D": {
+   "cases": {
+    "crop": {
+     "channels": 34,
+     "file": "zlp-shift1d-crop",
+     "offsetEV": 7.0
+    },
+    "nocrop": {
+     "channels": 40,
+     "file": "zlp-shift1d-nocrop",
+     "offsetEV": 5.0
+    }
+   },
+   "inputFile": "zlp-shift1d-input",
+   "offsetEV": 5.0,
+   "scaleEV": 0.5,
+   "shiftEV": [
+    0.0,
+    0.35,
+    -0.72,
+    1.6
+   ]
+  },
+  "truth": {
+   "globalOffsetEV": 0.37,
+   "zlpCentreEV": [
+    [
+     -0.7000000000000001,
+     -0.06,
+     0.37,
+     0.95
+    ],
+    [
+     1.28,
+     1.7999999999999998,
+     -1.0899999999999999,
+     0.64
+    ],
+    [
+     -0.44000000000000006,
+     0.49,
+     1.1,
+     0.18
+    ]
+   ],
+   "zlpFWHMEV": 0.9
+  }
+ }
+}
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diff --git a/tools/eels-task16/README.md b/tools/eels-task16/README.md
new file mode 100644
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--- /dev/null
+++ b/tools/eels-task16/README.md
@@ -0,0 +1,51 @@
+# tools/eels-task16: exSpy / HyperSpy pins for EELS task 16, sections 2, 3 and 4
+
+Written before the Swift code, so the Mac session that implements `docs/design/eels-task-16.md` starts with numbers.
+Covers zero-loss alignment and mask (design section 2), power-law extrapolation and Hanning taper (section 3), Fourier-log,
+Fourier-ratio and `optimal_fft_size` (section 4). Not covered: GOS tables, the edge model fit (section 6), Richardson-Lucy.
+
+```
+python -m venv v && v/bin/pip install hyperspy==2.4.0 exspy==0.3.2      # the design's pins; NumPy 2.5.4, SciPy 1.18.1 were used
+v/bin/python -I -B tools/eels-task16/pins.py                             # --out DIR to write elsewhere
+```
+The script asserts the two versions. Output: `Tests/SpectroEELSTests/Fixtures/eels16-pins.json` (the layout is the script's
+docstring) and 58 `eels16-*.f64` arrays (float64 little-endian, C order, NaN kept; shape and sha256 under `files` in the JSON), 2.8 MB.
+A second run is byte-identical (sha256 over all files checked). HyperSpy ran without numba (non-accelerated paths).
+The pins use exSpy 0.3.2 from PyPI, not the `7185a4d1` checkout the older EELS pins use; the design note names 0.3.2.
+
+## Inputs (all synthetic, deterministic, images are 3 x 4 pixels, pixel p = row * 4 + col)
+
+- **Alignment**: low loss 600 ch, -20 eV + 0.1 k; ZLP FWHM 0.9 eV at a per-pixel centre (global 0.37 eV plus -1.46 .. +1.43 eV,
+  none on a channel), plasmon at 15 eV, power-law tail. A second image with a spike larger than the ZLP at 12 eV, and a core-loss-like
+  image (300 ch, 100 eV + 0.5 k) for `also_align`. Truth: the planted centres.
+- **Power law**: A in 4e5 .. 3e12, r in -0.4 .. 4 (one pixel r < 0 for `fix_neg_r`), 200 ch from 300 eV at 0.5 eV, binned and unbinned.
+- **Plural scattering**: ZLP at 0 eV (FWHM 0.9), single-scattering shape S (peaks 12 and 24 eV), t/lambda 0.1 .. 1.1 per pixel,
+  I0 = 1e6, 1600 ch from -20 eV at 0.1 eV: J = I0 ifft(fft(Z/I0) exp(fft(S)/I0)) on an 8192 circular grid, cropped. Core loss: a
+  step-plus-exponential edge convolved with J/I0, 300 ch from 280 eV. Truth: S, S broadened by the ZLP, the edge.
+
+## Findings the port must know
+
+1. **`max_shift` is not tested here** (a no-op in `estimate_shift1D`, as the design says). `estimateShift` pins `estimate_shift1D`
+   with reference pixel 0, `number_of_interpolation_points` 0, 5 and 9, two windows.
+2. **A navigation mask given as an ndarray must have shape (nx, ny)**, the reverse of the data's (ny, nx), or exSpy raises; the pins pass it
+   as a signal (`BaseSignal(mask).T`), which is what the kit's `PixelMask` (row-major ny x nx) means. Masked pixels give NaN centres.
+3. **`align_zero_loss_peak` without `signal_range` on a spectrum with a spike** above the ZLP aligns on the spike (offset -32.0 eV, case
+   `spike-no-range`); with `signal_range=(-5, 5)` it does not. Both are pinned as exSpy behaves.
+4. **`shiftPasses`** hold the shift arrays `shift1D` received, in order: pass 1 is the coarse shift (`mean(zlpc) - zlpc`), pass 2 the
+   `align1D` subpixel shift (absent with `subpixel=False`; four entries with `also_align`, one per signal per pass).
+5. **Fourier-log returns S x Z/I0, not S**: `z * log(j/z)` is the single-scattering distribution broadened by the ZLP. Against that
+   truth the interior (outside the tapered channels) agrees to 5.6e-4 of the peak; the planted-truth test must compare with `plural-single-broadened`.
+   It needs the spectrum to decay inside the axis: with a truncated plural tail (first try) the error was 20 %.
+6. **Fourier-ratio carries a factor 1/scale**: exSpy's Gaussian is a density per eV (A = 1), so the result is the edge smoothed by the
+   Gaussian times 1/scale (10 here). The interior of `fr-fixed-threshold-6` equals smoothed truth / scale to 3 %. The port reproduces
+   exSpy, not the physics (parity row note).
+7. **Taper default**: `channels = max(20, round(0.02 n))`: 20 for every n < 1250, 40 at n = 2000, 100 at n = 5000 (cases `default-n*`).
+8. **`power_law_extrapolation` `fix_neg_r`** zeroes A where r <= 0: the JSON has `A` (estimate) and `AUsed`. A, r come from
+   `PowerLaw.estimate_parameters` on the zero-extended signal, so they depend on the window only, not on the extrapolation size (checked).
+
+## Not pinned here (left to the implementing session)
+
+`estimate_peak_width` on pathological spectra (not exactly two roots gives NaN; only the planted ZLP is pinned, in `fwhmAllPixelsEV`
+and each Fourier-ratio case's `fwhmEV`); `richardson_lucy_deconvolution`; the lazy (dask) code paths; Poisson-noisy inputs (the old
+slices' noisy pins hold counting statistics; deconvolution of noisy data is dominated by the `log`/division in Fourier space and is
+not a useful agreement test).
diff --git a/tools/eels-task16/parity-rows-draft.md b/tools/eels-task16/parity-rows-draft.md
new file mode 100644
index 0000000..62cb555
--- /dev/null
+++ b/tools/eels-task16/parity-rows-draft.md
@@ -0,0 +1,19 @@
+# Draft `docs/parity.md` rows for task 16 sections 2, 3, 4
+
+For the implementing session to move into `docs/parity.md` (design section 9) when the code lands; state stays "missing" until then.
+Columns as in parity.md. Fixture: `Tests/SpectroEELSTests/Fixtures/eels16-pins.json` (+ `eels16-*.f64`), generated by `tools/eels-task16/pins.py`
+(exSpy 0.3.2 / HyperSpy 2.4.0). "kit" = the tolerance the pins are to be held at; upstream = what exSpy's own test uses.
+
+| exSpy / HyperSpy | SpectroKit | state | code | priority | upstream tolerance (test file) | evidence (to write) |
+|---|---|---|---|---|---|---|
+| `estimate_zero_loss_peak_centre` (with `mask`, `signal_range`) | `EELSAlignment.zeroLossPeakCentre` | missing | TOL | study | `test_eels.py::test_estimate_zero_loss_peak_centre` defaults (rtol 1e-7); kit: exact eV (first argmax of a grid value) | `AlignPinsTests`: `zlp.centre.{plain,masked,spike}` |
+| `get_zero_loss_peak_mask` | `EELSAlignment.zeroLossPeakMask` | missing | exact | study | `test_eels.py::test_get_zero_loss_peak_mask*` exact | `zlp.mask` (widths 5.0, 2.0; with and without `signal_mask`) |
+| `Signal1D.estimate_shift1D` | `EELSAlignment.estimateShift` | missing | TOL | study | `test_1D_tools.py::TestAlignTools::test_estimate_shift` atol 1e-3 (eV); `max_shift` is a no-op upstream and is not offered | `zlp.estimateShift.{default,wide,ip0,ip9}` at atol 1e-3 eV |
+| `Signal1D.shift1D` | `EELSAlignment.shift` | missing | TOL | study | `test_1D_tools.py::TestAlignTools::test_shift1D` defaults; new offset exact | `zlp.shift1D.cases.{crop,nocrop}`: data at rtol 1e-7 atol 1e-12, offset and size exact, NaN where undefined |
+| `align_zero_loss_peak` (calibrate, subpixel, crop, mask, signal_range, also_align) | `EELSAlignment.alignZeroLossPeak` | missing | TOL | study | `test_eels.py::TestAlignZLP` mean/std of re-estimated centre defaults (rtol 1e-7; with mask atol eps); `calibrate=False` std atol 1e-2; `crop=False` size kept; spike signal_range max 8 | `zlp.align.*` (11 variants): offset, size, scale exact to 1e-12; data rtol 1e-7 atol 1e-9 x max; shift passes atol 1e-9 eV; truth: planted centres within 0.5 channel coarse, 1e-3 eV subpixel |
+| `Signal1D.hanning_taper` (side, channels, offset) | `EELSSpectrumOps.hanningTaper` | missing | exact | useful | no numeric test upstream; exact by construction (`np.hanning`) | `taper.cases.*`: returned channels exact, data to 1e-15 relative; default-channel rule `default-n*` |
+| `power_law_extrapolation` (window, size, `fix_neg_r`, binned) | `EELSSpectrumOps.powerLawExtrapolation` | missing | TOL | study | `test_eels.py::TestPowerLawExtrapolation` atol 1e-2 against the exact power law (`atol=10e-3`); `test_power_law.py` A, r defaults | `powerLaw.cases.*`: A, r rtol 1e-7; data rtol 1e-9; vs `exactFile` atol 1e-2 (binned and unbinned) |
+| `utils.math_tools.optimal_fft_size` / `scipy.fft.next_fast_len` | `EELSDeconvolution.optimalFFTSize` | missing | exact | useful | none upstream; exact integers | `optimalFFTSize` (217 values, real and complex) |
+| `fourier_log_deconvolution` (`add_zlp`, `crop`) | `EELSDeconvolution.fourierLog` | missing | TOL | study | none upstream (kit decision, design section 4): rtol 1e-7 + atol 1e-7 x max abs of the pinned result per pixel; `fftSize`, `taperedChannels` exact | `fourierLog.cases.*` (4); planted truth: interior vs S x Z/I0 within 6e-4 of the peak (exSpy's own number, finding 5) |
+| `fourier_ratio_deconvolution` (fwhm, threshold, extrapolate_*) | `EELSDeconvolution.fourierRatio` | missing | TOL | study | none upstream (`test_running` only runs): same rule; `fftSize`, tapered channels exact; FWHM to 1e-9 eV; I0 rtol 1e-12 | `fourierRatio.cases.*` (6); output carries exSpy's 1/scale factor (finding 6); planted truth: interior vs smoothed edge / scale within 3 % |
+| `estimate_peak_width` (`factor=0.5`) | part of `fourierRatio` (`FourierRatioOptions.fwhmEV == nil`) | missing | TOL | useful | `test_signal1d.py` peak-width tests (kit reads the roots as cubic-spline roots) | `fourierRatio.fwhmAllPixelsEV` at 1e-9 eV; NaN when not exactly two roots |
diff --git a/tools/eels-task16/pins.py b/tools/eels-task16/pins.py
new file mode 100644
index 0000000..a0b8666
--- /dev/null
+++ b/tools/eels-task16/pins.py
@@ -0,0 +1,408 @@
+#!/usr/bin/env python3
+"""exSpy / HyperSpy pins for SpectroKit EELS task 16, sections 2, 3 and 4 of docs/design/eels-task-16.md.
+
+Written before the Swift code. Pins what exSpy 0.3.2 / HyperSpy 2.4.0 answer on deterministic synthetic spectrum images with
+known shifts: zero-loss alignment and mask (section 2), power-law extrapolation and Hanning taper (section 3),
+Fourier-log and Fourier-ratio deconvolution and `optimal_fft_size` (section 4). Not covered: GOS tables, the edge model fit,
+Richardson-Lucy. Agreement with exSpy is agreement, not truth; the planted truth (shifts, edge shape) is stored beside each case.
+
+Run (any venv with `pip install hyperspy==2.4.0 exspy==0.3.2`; NumPy 2.5.4, SciPy 1.18.1 were used):
+
+    python -I -B tools/eels-task16/pins.py [--out DIR]
+
+Writes into --out (default Tests/SpectroEELSTests/Fixtures/):
+
+    eels16-<name>.f64   float64 little-endian, C order, NaN kept (named in eels16-pins.json under "files" with shape and sha256)
+    eels16-pins.json    everything else; floats are Python reprs (they round-trip exactly), NaN is null
+
+Images are (ny, nx, channels) = (3, 4, n), pixel p = row * 4 + col. Axis of channel k: offset + scale * k.
+Every output is byte-identical on a second run (default_rng(20261021); no other randomness).
+
+Layout of eels16-pins.json:
+  environment      versions, sha256 of this script, the generator command
+  files            name -> {shape, sha256} for every .f64
+  zlp.*            section 2. inputs: "ll" (shifted ZLP + plasmon + tail), "llSpike" (a spike larger than the ZLP at 12 eV),
+                   "core" (a second image carrying the same shifts, for also_align); truth: per-pixel ZLP centre in eV.
+      centre       estimate_zero_loss_peak_centre, with and without mask (masked -> null)
+      mask         get_zero_loss_peak_mask for widths 5.0 and 2.0, with and without signal_mask
+      estimateShift   estimate_shift1D(start, end, reference_indices=(0,0), number_of_interpolation_points=5) in eV
+      align        one record per align_zero_loss_peak variant: kwargs, offset, size, scale, the re-estimated centre of the
+                   aligned image, the shift arrays shift1D received in order (pass 1 coarse, pass 2 align1D subpixel), the
+                   aligned image file, the also_align image file where used
+      shift1D      shift1D on a ramp with fractional shifts, crop True and False: offset, size, data
+  taper            hanning_taper cases: side, channels, offset -> returned channels and tapered data
+  powerLaw         power_law_extrapolation cases (binned/unbinned, window, size, fix_neg_r): A, r from PowerLaw.estimate_parameters
+                   on the zero-extended signal, the extrapolated data, the exact power law at the new channels (truth)
+  optimalFFTSize   hyperspy.misc.math_tools.optimal_fft_size(n, real) for n in 1..200 plus selected larger n
+  fourierLog       cases: size, taperedChannels, result with add_zlp / crop False/True; planted truth (single scattering S)
+  fourierRatio     cases: size, fwhm (estimate_peak_width), thresholds, I0, taperedChannels, result; planted truth (edge)
+"""
+import argparse
+import hashlib
+import json
+import logging
+import math
+import os
+import platform
+import sys
+import warnings
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+REPO = os.path.normpath(os.path.join(HERE, "..", ".."))
+
+ap = argparse.ArgumentParser(description=__doc__.split("\n")[0])
+ap.add_argument("--out", default=os.path.join(REPO, "Tests", "SpectroEELSTests", "Fixtures"))
+ARGS = ap.parse_args()
+OUT = ARGS.out
+os.makedirs(OUT, exist_ok=True)
+
+logging.disable(logging.CRITICAL)
+warnings.simplefilter("ignore")
+
+import numpy as np                                   # noqa: E402
+import scipy                                         # noqa: E402
+import hyperspy                                      # noqa: E402
+import hyperspy.api as hs                            # noqa: E402
+import exspy                                         # noqa: E402
+from hyperspy.misc.math_tools import optimal_fft_size   # noqa: E402
+from hyperspy._signals.signal1d import Signal1D      # noqa: E402
+
+assert hyperspy.__version__ == "2.4.0" and exspy.__version__ == "0.3.2", (hyperspy.__version__, exspy.__version__)
+
+NY, NX = 3, 4
+RNG = np.random.default_rng(20261021)
+FILES = {}
+PINS = {}
+
+
+def jnum(x):
+    """float (or None) for JSON: NaN -> null."""
+    if x is None:
+        return None
+    x = float(x)
+    return None if math.isnan(x) else x
+
+
+def jlist(a):
+    a = np.asarray(a, dtype=np.float64)
+    if a.ndim == 0:
+        return jnum(a)
+    return [jlist(v) for v in a]
+
+
+def write(name, arr):
+    """Write eels16-<name>.f64 and record it; returns the array as float64 C-order."""
+    a = np.ascontiguousarray(np.asarray(arr, dtype="<f8"))
+    path = os.path.join(OUT, "eels16-%s.f64" % name)
+    a.tofile(path)
+    FILES[name] = {"shape": list(a.shape), "sha256": hashlib.sha256(a.tobytes()).hexdigest()}
+    return a
+
+
+def eels(data, offset, scale, binned=True, title="x"):
+    s = exspy.signals.EELSSpectrum(np.array(data, dtype=np.float64))
+    ax = s.axes_manager.signal_axes[0]
+    ax.offset = offset
+    ax.scale = scale
+    ax.units = "eV"
+    ax.is_binned = binned
+    s.metadata.General.title = title
+    return s
+
+
+def gauss(x, c, fwhm, area):
+    sg = fwhm / 2.3548200450309493
+    return area / (sg * math.sqrt(2 * math.pi)) * np.exp(-0.5 * ((x - c) / sg) ** 2)
+
+
+# ----------------------------------------------------------------------------------------------------------------- section 2
+# Shifted low-loss image: ZLP (FWHM 0.9 eV) at a per-pixel centre, a plasmon at 15 eV, a power-law tail.
+N_LL, OFF_LL, SC_LL = 600, -20.0, 0.1
+E_LL = OFF_LL + SC_LL * np.arange(N_LL)
+GLOBAL = 0.37
+CENTRES = (GLOBAL + np.array([[-1.07, -0.43, 0.0, 0.58], [0.91, 1.43, -1.46, 0.27], [-0.81, 0.12, 0.73, -0.19]])).astype(np.float64)
+AMP = 1e6 * (1 + 0.1 * np.arange(NY * NX).reshape(NY, NX) / 12)
+
+
+def lowloss_shifted(spike=False):
+    d = np.zeros((NY, NX, N_LL))
+    for i in range(NY):
+        for j in range(NX):
+            d[i, j] = (gauss(E_LL, CENTRES[i, j], 0.9, AMP[i, j]) + gauss(E_LL, 15.0, 4.0, 0.3 * AMP[i, j])
+                       + np.where(E_LL >= 2, 5e4 * np.maximum(E_LL, 2) ** -2.5, 0))
+            if spike:
+                d[i, j, int(round((12.0 - OFF_LL) / SC_LL))] = 3.0 * d[i, j].max()
+    return d
+
+
+ll = write("zlp-ll", lowloss_shifted())
+llspike = write("zlp-ll-spike", lowloss_shifted(spike=True))
+# A core-loss-like second image that carries the same shifts (also_align): 300 channels at 0.5 eV from 100 eV.
+N_CO, OFF_CO, SC_CO = 300, 100.0, 0.5
+core = np.stack([np.stack([1e4 * np.maximum(OFF_CO + SC_CO * np.arange(N_CO), 1) ** -1.5 * (1 + 0.1 * (i * NX + j)) for j in range(NX)]) for i in range(NY)])
+write("zlp-core", core)
+PINS["zlp"] = {
+    "ll": {"file": "zlp-ll", "nx": NX, "ny": NY, "channels": N_LL, "offsetEV": OFF_LL, "scaleEV": SC_LL},
+    "llSpike": {"file": "zlp-ll-spike", "spikeEV": 12.0},
+    "core": {"file": "zlp-core", "channels": N_CO, "offsetEV": OFF_CO, "scaleEV": SC_CO},
+    "truth": {"zlpCentreEV": jlist(CENTRES), "globalOffsetEV": GLOBAL, "zlpFWHMEV": 0.9},
+}
+
+MASK = np.zeros((NY, NX), dtype=bool)
+MASK[0, 1] = MASK[2, 2] = True
+
+
+def nav_mask(m):
+    """exSpy wants a navigation mask as a signal with signal dimension 0 (an ndarray is compared with (nx, ny))."""
+    return None if m is None else hs.signals.BaseSignal(np.asarray(m)).T
+
+
+def fresh(kind="ll"):
+    d = {"ll": ll, "llSpike": llspike}[kind]
+    return eels(d, OFF_LL, SC_LL, title=kind)
+
+
+centre = {}
+for name, kind, mask in [("plain", "ll", None), ("masked", "ll", MASK), ("spike", "llSpike", None)]:
+    c = fresh(kind).estimate_zero_loss_peak_centre(mask=nav_mask(mask))
+    centre[name] = jlist(c.data)
+PINS["zlp"]["centre"] = centre
+
+zmask = {}
+for width in (5.0, 2.0):
+    for sm_name, sm in [("none", None), ("signal", (E_LL > 30))]:
+        m = fresh().get_zero_loss_peak_mask(zero_loss_peak_mask_width=width, signal_mask=sm)
+        zmask["w%.1f-%s" % (width, sm_name)] = {"mask": [bool(v) for v in m], "signalMask": None if sm is None else [bool(v) for v in sm]}
+PINS["zlp"]["mask"] = zmask
+
+est = {}
+for name, (a, b, ip) in {"default": (-3.0, 3.0, 5), "wide": (-4.0, 4.0, 5), "ip0": (-3.0, 3.0, 0), "ip9": (-3.0, 3.0, 9)}.items():
+    s = fresh()
+    ref = s.estimate_shift1D(a, b, reference_indices=(0, 0), number_of_interpolation_points=ip, show_progressbar=False)
+    est[name] = {"fromEV": a, "toEV": b, "interpolationPoints": ip, "shiftEV": jlist(ref)}
+PINS["zlp"]["estimateShift"] = est
+
+# align_zero_loss_peak variants. shift1D is wrapped to record the shift arrays it receives, in order.
+RECORD = []
+_orig_shift = Signal1D.shift1D
+
+
+def _wrapped(self, shift_array, *a, **k):
+    RECORD.append(np.array(shift_array, dtype=np.float64).copy())
+    return _orig_shift(self, shift_array, *a, **k)
+
+
+Signal1D.shift1D = _wrapped
+VARIANTS = {
+    "default": dict(kind="ll", kw={}),
+    "no-subpixel": dict(kind="ll", kw=dict(subpixel=False)),
+    "no-calibrate": dict(kind="ll", kw=dict(calibrate=False)),
+    "no-crop": dict(kind="ll", kw=dict(crop=False)),
+    "no-crop-no-calibrate": dict(kind="ll", kw=dict(crop=False, calibrate=False)),
+    "mask": dict(kind="ll", kw=dict(mask=MASK)),
+    "signal-range": dict(kind="ll", kw=dict(signal_range=(-5.0, 5.0))),
+    "spike-no-range": dict(kind="llSpike", kw={}),
+    "spike-range": dict(kind="llSpike", kw=dict(signal_range=(-5.0, 5.0))),
+    "also-align": dict(kind="ll", kw={}, also=True),
+    "interp-ip3": dict(kind="ll", kw=dict(number_of_interpolation_points=3)),
+}
+align = {}
+for name, v in VARIANTS.items():
+    s = fresh(v["kind"])
+    also = [eels(core, OFF_CO, SC_CO, title="core")] if v.get("also") else []
+    RECORD.clear()
+    kw = dict(v["kw"])
+    if "mask" in kw:
+        kw["mask"] = nav_mask(kw["mask"])
+    s.align_zero_loss_peak(also_align=also, print_stats=False, show_progressbar=False, **kw)
+    ax = s.axes_manager.signal_axes[0]
+    rec = {"kind": v["kind"], "kwargs": {k: (None if k == "mask" else (list(x) if isinstance(x, tuple) else x)) for k, x in v["kw"].items()},
+           "maskUsed": "mask" in v["kw"],
+           "offsetEV": float(ax.offset), "scaleEV": float(ax.scale), "channels": int(ax.size),
+           "reestimatedCentreEV": jlist(s.estimate_zero_loss_peak_centre(mask=kw.get("mask")).data),
+           "shiftPasses": [jlist(r) for r in RECORD],
+           "file": "zlp-align-%s" % name}
+    write(rec["file"], s.data)
+    if also:
+        cax = also[0].axes_manager.signal_axes[0]
+        rec["alsoAligned"] = {"file": "zlp-align-%s-core" % name, "offsetEV": float(cax.offset), "channels": int(cax.size)}
+        write(rec["alsoAligned"]["file"], also[0].data)
+    align[name] = rec
+Signal1D.shift1D = _orig_shift
+PINS["zlp"]["align"] = align
+
+# shift1D alone: a ramp-plus-bump signal, fractional shifts in channels * scale (eV).
+ramp = np.array([np.sin(np.arange(40) / 5.0) + 0.05 * np.arange(40) * (k + 1) for k in range(4)])   # (4, 40)
+sh = np.array([0.0, 0.35, -0.72, 1.6])                                                             # eV, scale 0.5 -> 0, 0.7, -1.44, 3.2 channels
+shift = {}
+for crop in (True, False):
+    s = eels(ramp, 5.0, 0.5, binned=False)
+    s.shift1D(sh, crop=crop, show_progressbar=False)
+    ax = s.axes_manager.signal_axes[0]
+    shift["crop" if crop else "nocrop"] = {"offsetEV": float(ax.offset), "channels": int(ax.size), "file": "zlp-shift1d-%s" % ("crop" if crop else "nocrop")}
+    write(shift["crop" if crop else "nocrop"]["file"], s.data)
+write("zlp-shift1d-input", ramp)
+PINS["zlp"]["shift1D"] = {"inputFile": "zlp-shift1d-input", "offsetEV": 5.0, "scaleEV": 0.5, "shiftEV": jlist(sh), "cases": shift}
+
+# --------------------------------------------------------------------------------------------------------------- section 3
+# Hanning taper (HyperSpy Signal1D.hanning_taper).
+taper = {}
+tdata = 1.0 + np.arange(2 * 300).reshape(2, 300) * 0.01 + 5.0
+write("taper-input", tdata)
+for name, kw in {"both": {}, "left": dict(side="left"), "right": dict(side="right"), "channels25": dict(channels=25),
+                 "offset10": dict(offset=10), "left-ch40-off5": dict(side="left", channels=40, offset=5)}.items():
+    s = eels(tdata, 0.0, 1.0)
+    n = s.hanning_taper(**kw)
+    taper[name] = {"kwargs": kw, "taperedChannels": int(n), "file": "taper-%s" % name}
+    write(taper[name]["file"], s.data)
+for n in (50, 100, 999, 1024, 2000, 5000):                      # default channels = max(20, round(0.02 n))
+    s = eels(np.ones((1, n)), 0.0, 1.0)
+    taper["default-n%d" % n] = {"kwargs": {}, "n": n, "taperedChannels": int(s.hanning_taper())}
+PINS["taper"] = {"input": {"file": "taper-input", "channels": 300, "rows": 2}, "cases": taper}
+
+# Power-law extrapolation (exSpy power_law_extrapolation).
+N_PL, OFF_PL, SC_PL = 200, 300.0, 0.5
+E_PL = OFF_PL + SC_PL * np.arange(N_PL)
+A_PL = np.array([[1e9, 5e8, 2e10], [3e12, 8e7, 4e5]])
+R_PL = np.array([[3.0, 2.5, 3.5], [4.0, 1.7, -0.4]])        # last pixel: r < 0 (rising) for fix_neg_r
+pl = {}
+for binned in (True, False):
+    d = A_PL[..., None] * E_PL ** (-R_PL[..., None]) * (SC_PL if binned else 1.0)
+    write("pl-input-%s" % ("binned" if binned else "unbinned"), d)
+    for ws, es, fix in [(20, 1024, False), (20, 100, True), (50, 100, False), (20, 100, False)]:
+        s = eels(d, OFF_PL, SC_PL, binned=binned)
+        out = s.power_law_extrapolation(window_size=ws, extrapolation_size=es, fix_neg_r=fix)
+        # A, r exactly as exSpy gets them: PowerLaw.estimate_parameters on the zero-extended copy over the last window
+        ext = s.deepcopy()
+        ext.data = np.zeros(list(d.shape[:-1]) + [N_PL + es])
+        ext.data[..., :N_PL] = d
+        ext.get_dimensions_from_data()
+        comp = hs.model.components1D.PowerLaw()
+        comp._axes_manager = s.axes_manager
+        ax = s.axes_manager.signal_axes[0]
+        A, r = comp.estimate_parameters(ext, ax.index2value(ax.size - ws), ax.index2value(ax.size - 1), out=True)
+        name = "%s-w%d-e%d%s" % ("binned" if binned else "unbinned", ws, es, "-fixneg" if fix else "")
+        e_new = OFF_PL + SC_PL * np.arange(N_PL, N_PL + es)
+        exact = A_PL[..., None] * e_new ** (-R_PL[..., None]) * (SC_PL if binned else 1.0)
+        pl[name] = {"binned": binned, "windowChannels": ws, "extrapolationChannels": es, "fixNegativeR": fix,
+                    "A": jlist(A), "AUsed": jlist(np.where(r <= 0, 0, A) if fix else A), "r": jlist(r), "inputFile": "pl-input-%s" % ("binned" if binned else "unbinned"),
+                    "file": "pl-%s" % name, "exactFile": "pl-exact-%s" % name, "channels": int(out.axes_manager.signal_axes[0].size)}
+        write(pl[name]["file"], out.data)
+        write(pl[name]["exactFile"], exact)
+PINS["powerLaw"] = {"offsetEV": OFF_PL, "scaleEV": SC_PL, "channels": N_PL, "truthA": jlist(A_PL), "truthR": jlist(R_PL), "cases": pl}
+
+# --------------------------------------------------------------------------------------------------------------- section 4
+PINS["optimalFFTSize"] = {
+    "ns": [int(n) for n in list(range(1, 201)) + [255, 256, 257, 511, 1000, 1023, 1024, 1025, 1500, 2047, 2048, 2049, 2200, 4093, 4097, 10007, 65537]],
+}
+PINS["optimalFFTSize"]["real"] = [int(optimal_fft_size(n, True)) for n in PINS["optimalFFTSize"]["ns"]]
+PINS["optimalFFTSize"]["complex"] = [int(optimal_fft_size(n, False)) for n in PINS["optimalFFTSize"]["ns"]]
+
+# Planted plural-scattering low loss: ZLP at 0 eV for every pixel, thickness t/lambda per pixel, J = I0 ifft(Z' exp(fft S / I0)).
+N_P, OFF_P, SC_P = 1600, -20.0, 0.1                                     # -20 .. 139.9 eV, long enough that the plural tail has decayed
+E_P = OFF_P + SC_P * np.arange(N_P)
+TAU = np.array([[0.2, 0.4, 0.6, 0.8], [1.0, 1.2, 0.1, 0.3], [0.5, 0.7, 0.9, 1.1]])
+I0_P = 1e6
+PAD = 8192                                                              # circular grid long enough that nothing wraps
+z1 = gauss(E_P, 0.0, 0.9, 1.0)                                          # unit-area ZLP per eV
+S1 = gauss(E_P, 12.0, 4.0, 1.0) + gauss(E_P, 24.0, 7.0, 0.5)           # single-scattering shape (unit area 1.5)
+S1 = np.where(E_P > 2.0, S1, 0.0)
+zl = np.zeros((NY, NX, N_P))
+jl = np.zeros((NY, NX, N_P))
+ss = np.zeros((NY, NX, N_P))
+for i in range(NY):
+    for j in range(NX):
+        tau = TAU[i, j]
+        S = tau * I0_P * S1 / S1.sum() * 1.0                            # counts: area tau * I0 over the channels
+        Z = I0_P * z1 / z1.sum()                                        # counts: area I0
+        Zf, Sf = np.fft.rfft(Z, PAD), np.fft.rfft(S, PAD)
+        J = np.fft.irfft(Zf * np.exp(Sf / I0_P), PAD)[:N_P]
+        zl[i, j], jl[i, j], ss[i, j] = Z, J, S
+write("plural-zlp", zl)
+write("plural-ll", jl)
+write("plural-single", ss)
+# Fourier-log returns Z (x) S / I0 (the single-scattering distribution broadened by the ZLP), not S: that is the truth to compare with
+ssb = np.stack([np.stack([np.convolve(ss[i, j], zl[i, j] / zl[i, j].sum())[:N_P] for j in range(NX)]) for i in range(NY)])
+write("plural-single-broadened", ssb)
+plural = {"nx": NX, "ny": NY, "channels": N_P, "offsetEV": OFF_P, "scaleEV": SC_P, "tauOverLambda": jlist(TAU), "i0": I0_P,
+          "zlpFile": "plural-zlp", "lowLossFile": "plural-ll", "singleScatteringFile": "plural-single", "singleScatteringBroadenedFile": "plural-single-broadened",
+          "note": "J = I0 ifft(fft(Z/I0) exp(fft(S)/I0)) on a 8192 circular grid, cropped; truth S is the single-scattering counts, S x Z/I0 is what Fourier-log returns"}
+
+fl = {}
+for name, kw in {"default": {}, "add-zlp": dict(add_zlp=True), "crop": dict(crop=True), "add-zlp-crop": dict(add_zlp=True, crop=True)}.items():
+    j = eels(jl, OFF_P, SC_P, title="J")
+    z = eels(zl, OFF_P, SC_P, title="Z")
+    tapped = j.deepcopy().hanning_taper()
+    out = j.fourier_log_deconvolution(z, **kw)
+    size = optimal_fft_size(N_P + N_P - 1, True)
+    ax = out.axes_manager.signal_axes[0]
+    fl[name] = {"kwargs": kw, "fftSize": int(size), "taperedChannels": int(tapped), "channels": int(ax.size),
+                "offsetEV": float(ax.offset), "file": "fl-%s" % name}
+    write(fl[name]["file"], out.data)
+# zlp shorter than the spectrum and longer than it (sizes differ; zlp.data is broadcast against j only when sizes match,
+# so the shapes here keep the channel counts equal and the case documents that exSpy requires it)
+PINS["fourierLog"] = {"plural": plural, "cases": fl}
+
+# Fourier ratio: core loss = edge (single scattering, background removed) convolved with J/I0 (ZLP weight 1), 300 channels at 0.1 eV from 280 eV.
+N_C, OFF_C = 300, 280.0
+e = np.arange(N_C) * SC_P
+edge = np.where(e >= 4.0, 2e3 * np.exp(-(e - 4.0) / 25.0), 0.0)         # a smooth step with an exponential tail, counts per channel
+core_p = np.zeros((NY, NX, N_C))
+edge_p = np.zeros((NY, NX, N_C))
+ZERO = int(round(-OFF_P / SC_P))                                        # channel of 0 eV in the low loss
+for i in range(NY):
+    for j in range(NX):
+        ed = edge * (1.0 + 0.2 * (i * NX + j))
+        full = np.convolve(ed, jl[i, j] / I0_P)
+        core_p[i, j] = full[ZERO:ZERO + N_C]
+        edge_p[i, j] = ed
+write("plural-core", core_p)
+write("plural-edge", edge_p)
+fr = {}
+for name, kw in {"default": {}, "fixed-threshold-6": dict(threshold=6.0), "fwhm-1.5": dict(fwhm=1.5, threshold=6.0),
+                 "no-extrap-ll": dict(threshold=6.0, extrapolate_lowloss=False),
+                 "no-extrap-cl": dict(threshold=6.0, extrapolate_coreloss=False),
+                 "no-extrap": dict(threshold=6.0, extrapolate_lowloss=False, extrapolate_coreloss=False)}.items():
+    c = eels(core_p, OFF_C, SC_P, title="core")
+    l = eels(jl, OFF_P, SC_P, title="J")
+    kws = dict(kw)
+    ctx = {}
+    # the pieces exSpy computes internally, recomputed with the same calls
+    ll2 = l.power_law_extrapolation(window_size=100, extrapolation_size=100) if kw.get("extrapolate_lowloss", True) else l.deepcopy()
+    cl2 = c.power_law_extrapolation(window_size=20, extrapolation_size=100) if kw.get("extrapolate_coreloss", True) else c.deepcopy()
+    tap_ll, tap_cl = ll2.hanning_taper(), cl2.hanning_taper()
+    size = optimal_fft_size(ll2.axes_manager.signal_axes[0].size + cl2.axes_manager.signal_axes[0].size - 1)
+    thr = kw.get("threshold")
+    thr_used = l.estimate_elastic_scattering_threshold() if thr is None else None
+    I0 = ll2.estimate_elastic_scattering_intensity(threshold=thr_used if thr is None else thr)
+    fwhm_ref = float(l.get_current_signal().estimate_peak_width()._get_current_data()[0]) if kw.get("fwhm") is None else kw["fwhm"]
+    out = c.fourier_ratio_deconvolution(l, **kws)
+    fr[name] = {"kwargs": kw, "fftSize": int(size), "lowLossChannelsAfterExtrapolation": int(ll2.axes_manager.signal_axes[0].size),
+                "coreLossChannelsAfterExtrapolation": int(cl2.axes_manager.signal_axes[0].size),
+                "taperedChannelsLowLoss": int(tap_ll), "taperedChannelsCoreLoss": int(tap_cl),
+                "fwhmEV": jnum(fwhm_ref), "thresholdEV": None if thr_used is None else jlist(thr_used.data),
+                "i0": jlist(I0.data), "channels": int(out.axes_manager.signal_axes[0].size), "offsetEV": float(out.axes_manager.signal_axes[0].offset),
+                "file": "fr-%s" % name}
+    write(fr[name]["file"], out.data)
+# FWHM of every pixel's ZLP (estimate_peak_width on the whole image; NaN where the cubic spline does not have exactly two roots)
+fw = eels(jl, OFF_P, SC_P).estimate_peak_width()
+fwhm_all = jlist(fw.data)
+PINS["fourierRatio"] = {"note": "exSpy's Gaussian is a density per eV (A=1, sum over channels = 1/scale), so the result is the planted edge "
+                        "smoothed by the Gaussian AND multiplied by 1/scale: interior of fr-fixed-threshold-6 equals smoothed truth / scale to 3 %",
+                        "plural": plural, "core": {"file": "plural-core", "channels": N_C, "offsetEV": OFF_C, "scaleEV": SC_P,
+                                                   "truthEdgeFile": "plural-edge", "zeroLossChannel": ZERO},
+                        "fwhmAllPixelsEV": fwhm_all, "cases": fr}
+
+# ----------------------------------------------------------------------------------------------------------------- environment
+with open(__file__, "rb") as fh:
+    PINS["environment"] = {
+        "exspy": exspy.__version__, "hyperspy": hyperspy.__version__, "numpy": np.__version__, "scipy": scipy.__version__,
+        "python": platform.python_version(), "scriptSha256": hashlib.sha256(fh.read()).hexdigest(),
+        "command": "python -I -B tools/eels-task16/pins.py",
+        "note": "spectra are synthetic and deterministic; HyperSpy ran without numba (non-accelerated paths, identical results)",
+    }
+PINS["files"] = FILES
+with open(os.path.join(OUT, "eels16-pins.json"), "w") as fh:
+    json.dump(PINS, fh, indent=1, sort_keys=True, allow_nan=False)
+    fh.write("\n")
+print("wrote", len(FILES), "arrays")