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README.md

@@ -0,0 +1,132 @@
+---
+license: cc-by-4.0
+task_categories: [other]
+tags: [mri, diffusion-mri, monte-carlo, microstructure, replay-pack, rpk, restricted-diffusion]
+pretty_name: Canonical Pores — Monte-Carlo Replay Packs
+---
+
+# Canonical Pores — Monte-Carlo Replay Packs
+
+Converged Monte-Carlo diffusion walks in the three geometries that have exact analytical solutions —
+**parallel planes, cylinders, spheres** — frozen so that **any** acquisition can be computed afterwards
+without re-simulating.
+
+**600 substrates**: 200 diameters per shape, **0.1–20.0 µm in 0.1 µm steps**, each walked to
+**T = 200 ms** at D₀ = 2.0×10⁻⁹ m²/s. One `.rpk` (safetensors) per substrate.
+
+## What you can replay
+
+A replay pack is not a lookup table of pre-computed signals. It stores the walk itself, so the forward
+model is evaluated at read time:
+
+| you supply | how it is handled | exact? |
+|---|---|---|
+| **any gradient waveform** `G(t)` — PGSE, OGSE, PGSTE, CPMG-with-gradients, b-tensor (STE/PTE), arbitrary | projected onto the pack's temporal basis; the gradient phase is *linear* in position, so Parseval applies | exact for waveform content within the stored bands |
+| **surface relaxivity** ρ, any value | the pack's boundary-local-time channel, replayed | **exact** — not a mean-field `exp(-TE·ρ·S/V)` tag-on |
+| **per-compartment T₁ / T₂** | compartment map + relaxation log-weights | exact |
+| **any b-value, Δ, δ, direction, orientation** | consequences of the waveform above | — |
+
+There is **no short-pulse (SGP) and no Gaussian-phase approximation** anywhere in that path. That is the
+point of the dataset: the analytical models (`P2`–`P5`, `C2`–`C5`, `S2`–`S5` in
+[dmipy-fit](https://github.com/dmrai-lab/dmipy-fit)) each hold under some acquisition assumption; replay
+holds for the acquisition you actually ran.
+
+**Not in these packs**: susceptibility / off-resonance (no field channel), magnetization transfer, and
+diffusivity is fixed per pack — D₀ is baked into the walk, not a replay knob. (Time-rescaling to a
+different D₀ is a planned extension.)
+
+## What has been *certified*, and what that does not mean
+
+Every substrate's replay was compared against the exact eigenmode (matrix-method) solution and sized until
+the worst residual met **ε = 5×10⁻³**, measured over a battery of PGSE acquisitions:
+(δ, Δ) ∈ {(10,20), (10,40), (10,60), (10,100), (5,40)} ms × b ∈ {1, 3, 5}×10⁹ s/m², plus a
+surface-relaxivity battery. Walker counts were **measured**, never extrapolated: each candidate count was
+replayed and compared to the analytic reference on up to five *disjoint* blocks, all of which had to pass.
+
+**That battery is where the bound was measured — it is not a limit on what the pack replays.** The
+distinction matters in one direction only: a waveform whose temporal content falls outside the tested
+spectral range (very high-frequency OGSE, pulses shorter than the save grid) is still *replayable*, but its
+error is not covered by the quoted ε. For these three geometries you can settle that yourself — the exact
+analytical model ships in dmipy-fit (`P5PlaneMatrixMethod`, `C5CylinderMatrixMethod`,
+`S5SphereMatrixMethod`), so any acquisition you care about can be checked directly against ground truth.
+That is precisely what makes this dataset the validity proof for replay on substrates where no analytic
+answer exists.
+
+Practical resolution limits: the save grid is n_t ∈ {2000, 4000, 8000} over 200 ms, so features finer than
+that grid are not resolved; and the position codec keeps K ∈ {128, 196} temporal bands, which bounds the
+waveform bandwidth represented.
+
+| shape | substrates | all meet ε=5e-3 | worst residual |
+|---|---|---|---|
+| plane | 200 | ✅ | see `manifest.json` |
+| cylinder | 200 | ✅ | see `manifest.json` |
+| sphere | 200 | ✅ | see `manifest.json` |
+
+Each pack carries its own certification in metadata (`grid.worst_residual`, `grid.ladder`), so no consumer
+has to trust this table.
+
+## Tiers: fetch only what you need
+
+Two independent selections, and they **compose into a single contiguous byte range** — verified against
+HuggingFace range requests (`Accept-Ranges: bytes`, HTTP 206).
+
+**1. Precision (walkers).** Walkers are the leading axis of every per-walker tensor, and any prefix is an
+unbiased sub-ensemble with floor ∝ 1/√n. Each pack ships the **measured** prefix length for each floor:
+
+```python
+grid["prefix_tiers"]   # e.g. {"0.03": 1000, "0.02": 1000, "0.01": 1000, "0.005": 1000}
+```
+
+**2. Spatial axis.** Positions are stored as **one tensor per axis** (`pos_x`, `pos_y`, `pos_z`, each
+`(n_walkers, K)`), so you fetch only the components your geometry needs — a slab restricts one direction
+(the other two are free and analytic), a cylinder two, a sphere three. All three are always present, so
+rotating / b-tensor encodings that need the joint trajectory lose nothing.
+
+Measured on a 17.36 MiB pack: one axis + a 2,000-walker prefix = **0.49 MiB, a 36× reduction**.
+
+```python
+from safetensors import safe_open
+with safe_open("cylinder/d10.00um.rpk", framework="np") as f:
+    x = f.get_slice("pos_x")[0:2000]        # one axis, coarse tier: one contiguous read
+```
+
+**Status of the two selections.** Both are real and verified at the byte level, but only one is automatic
+today:
+
+* **Per-diameter fetch is automatic.** The `X6` compartments resolve a fitted diameter to the two
+  bracketing packs and download only those, so a fit transfers ~tens of MiB, never the dataset.
+* **Coarser-ε prefix fetch is manual.** The loader calls `hf_hub_download`, which retrieves whole files.
+  If you want a coarser floor you can range-read the prefix yourself as above — the metadata tells you how
+  many rows — but `X6` will not do it for you yet. It matters mainly for the 184 packs above 50 MiB: at
+  ε=1e-2 the whole dataset is 24.0 GiB against 7.96 GiB of actually-needed rows, and the largest packs
+  need a quarter of their rows (a two-hundredth at ε=3e-2).
+
+## Usage
+
+```python
+from dmipy_sim import read_rpk, compile_scheme, replay_signal
+pack = read_rpk("cylinder/d05.00um.rpk")
+W = compile_scheme(G, dt, pack.meta["compression"]["K"])   # G: (n_meas, n_t, 3), any waveform
+E = replay_signal(pack, W)                                  # + rho_over_D= for surface relaxivity
+```
+
+As fit compartments (`X6`), with the same parameters as their analytic siblings:
+
+```python
+from dmipy_fit.signal_models.cylinder_models import C6MonteCarloReplayCylinder
+model = C6MonteCarloReplayCylinder()        # mu, lambda_par, diameter — fetches packs on demand
+```
+
+`manifest.json` lists every substrate with its walker count, size, certified residual and prefix tiers.
+
+## Layout
+
+```
+canonical/D0-2.00e-9/{plane,cylinder,sphere}/d<NN.NN>um.rpk
+manifest.json
+```
+
+## Citation
+
+Generated with [`dmipy-sim`](https://github.com/dmrai-lab/dmipy-sim). Please cite the dataset DOI and the
+dmipy-sim replay-pack reference. CC-BY-4.0.

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