Card: cross-sections, analytic validation, B0 rotation, and a runnable reproduction snippet

README.md

@@ -15,6 +15,12 @@ acquisition can be computed afterwards without re-simulating.
 them under CC-BY-4.0. This dataset contributes the computation and a documented, self-certifying container.
 Meshes are used as published — full length, no cropping, smoothing or re-meshing.
 
+![axon cross-sections](figures/fig_substrate.png)
+
+*Cross-sections of `axon06` along its length, plus a 3-D view. Axon (inner) and myelin (outer) surfaces as
+published — the calibre and tortuosity vary along the fibre, which is the morphology under study.
+Generated by `report_assets.fig_substrate`.*
+
 ## What you can replay
 
 A replay pack stores the walk, not a table of pre-computed signals, so the forward model is evaluated at
@@ -34,6 +40,7 @@ read time:
 packs/axonNN.rpk         29 replay packs   (~71 MB each)
 field/axonNN.field.rpk   29 susceptibility field companions, masked (14–36 MB each)
 manifest.json            per-substrate metadata + SHA-256
+figures/                 the figures on this page, and the scripts that make them
 ```
 
 Total 2.54 GiB. The field companions are stored **masked** — an axon meanders, so a bounding box around it
@@ -59,16 +66,83 @@ would incur is a property you can read, not one you have to trust.
 Quote the **per-axon** floor rather than a dataset-wide number: it spans 4× across the set because it
 tracks each substrate's own internal-gradient variance, not the compression.
 
-## Seeding
+## Is the physics right?
+
+Against an **exact** answer, not against another simulation. For an infinite coaxial hollow cylinder the
+field inside the lumen is **exactly zero** at every orientation, and the sheath field is closed-form
+`ΔB/B₀ = χ[−1/6 + ½(R_i²/r²)cos 2φ]`. Any deviation is discretisation error with no fitting freedom.
+
+![analytic validation](figures/fig_analytic_validation.png)
+
+| | measured | exact |
+|---|---|---|
+| lumen field | **0.131%** of χ·B₀ | 0 |
+| sheath amplitude | **0.9996×** analytic | 1 |
+| sheath structure | **\|corr\| 0.9995** | 1 |
+
+This is a permanent gate in the generator's test suite (`test_susceptibility_field_oracle.py`), not a
+one-off check. It is what pins the **absolute** field amplitude — a hard binary myelin source rings into
+the lumen at ~2.6% of χ·B₀ through the non-decaying dipole kernel, which would silently inflate
+intra-axonal dephasing; partial-volume occupancy suppresses it to ~0.1%.
+
+## Susceptibility dephasing vs B₀ orientation
+
+![B0 rotation](figures/fig_b0_rotation.png)
+
+Intra-axonal spin-echo signal at b = 0 as B₀ rotates from parallel to the fibre (0°) to perpendicular
+(90°) — no diffusion weighting, so this isolates the susceptibility dephasing. Every one of the 29 axons
+is shown.
+
+The angular dependence matches the source study in shape (both minimise at 90°). The **magnitude differs**:
+contrast 0.037 here against 0.015 published, i.e. ~2.4× more attenuation at 90°. That comparison, and the
+field-solver question it raises, is analysed separately rather than resolved on this page — note only that
+the two are validated against different references, and the closed-form check above is the one with an
+exact answer.
+
+## Reproduce the curve yourself
+
+The figure above is not stored — it is **computed from one pack at read time**. This is the whole point of
+the format, so here it is in full:
+
+```python
+import numpy as np
+from huggingface_hub import hf_hub_download
+from dmipy_sim import bank
+from dmipy_sim.bank import read_rpk
+
+path = hf_hub_download("SubstrateCommons/winther-g6-axons", "packs/axon06.rpk",
+                       repo_type="dataset")
+pk = read_rpk(path)
+TE = (pk.n_t - 1) * pk.dt
+
+class B0Only:                       # b = 0: isolate the susceptibility dephasing
+    G = np.zeros((1, pk.n_t, 3))
+    dt = pk.dt
+
+signal = []
+for deg in (0, 15, 30, 45, 60, 75, 90):
+    t = np.deg2rad(deg)
+    s = bank.replay_susc(pk, B0Only, b0_dir=[np.sin(t), 0.0, np.cos(t)],
+                         B0=7.0, chi_iso=1.06e-6, refocus_time=TE / 2,
+                         relaxation=False, complex_signal=True, compartment=1)
+    signal.append(float(np.real(s[0])))
+
+print([round(x, 4) for x in signal])
+# [0.9243, 0.9337, 0.9457, 0.9462, 0.9322, 0.9159, 0.9121]
+```
+
+Nothing in that loop was decided when the pack was built. `B0=7.0` could be 3, `chi_iso` could be anything
+including an anisotropic component, `compartment=1` could be the myelin pool, `B0Only.G` could be any
+gradient waveform you like, and `refocus_time` places the spin echo wherever you want it. Each is a
+parameter of the **replay**, not of the simulation — which is why one 71 MB file answers a question nobody
+asked when it was written. Requires `pip install dmipy-sim`.
 
-The intra-axonal pool is seeded by an **exact ray-parity containment test**. An earlier unpublished build
-used a nearest-triangle test whose sidedness is only reliable close to a surface; over a padded box it
-accepted 13.6% of its points outside the lumen, at a median 10.2 µm from a wall bounding a radius of at
-most 1.24 µm — roughly 15% of that intra pool was unrestricted free water. Those packs were never released.
+## Seeding and confinement
 
-Confinement here, judged against independent ray parity rather than the seeding test: of 509 genuinely
-interior seeds, 1.4% lie outside at TE, and those end 0.07 µm beyond the wall — within the one-triangle
-accuracy of the test that measures them.
+The intra-axonal pool is seeded by an **exact ray-parity containment test**, and confinement is verified
+against independent ray parity rather than against the seeding test itself: of 509 genuinely interior
+seeds, 1.4% lie outside the surface at TE, and those end 0.07 µm beyond the wall — within the
+one-triangle accuracy of the test that measures them.
 
 ## Citation