wm_datasets README: wm_full_x0_zprior row + zprior section

wm_datasets/README.md

@@ -20,7 +20,7 @@ repo **[andreu-collabs/flow-abstract-wm-policies](https://huggingface.co/andreu-
 Full on-disk format: [`wm_datasets/documentation_wm_dataset.md`](wm_datasets/documentation_wm_dataset.md).
 The shards live under `wm_datasets/`.
 
-## The four datasets
+## The datasets
 
 Each is **10 seed shards × 512 episodes × 25 actions** (≈128k transitions), rendered at
 **256×256** — the `full` pair at **4-camera RGBD** (`top_down`/`wrist`/`side`/`front` + metric
@@ -41,12 +41,52 @@ incidentally nudges a neighboring block (support unchanged) no longer masks the
 | `wm_pp_x0` | `_s100…109` | pick_place only | X⁰ | `pp-fullH-xattn-branch-ot-60k` → `pp_x0/` |
 | `wm_pp_oracle` | `_s100…109` | pick_place only | X⁰ + y | `pp-oracle-fullH-xattn-ytok` → `pp_oracle/` |
 | `wm_full_oracle_zprior` | `_s200…203` | pick_place + stack + unstack | X⁰ + y, **z stored** | `full-oracle-xattn-ytok-100k` → `full_oracle/` + `latent_action_full_oracle_z2/` |
-
-`wm_full_oracle_zprior`: actions are `z ~ N(0, I)` drawn from the z2 VAE's prior and decoded to X⁰
-through the frozen flow (`--latent-run`), with the sampled `z` stored in `actions/z` (M, 2) f32 —
-the only shards carrying `z`. A z-native WM must read `actions/z` directly, not re-encode `x1`.
-Useful frac 0.953–0.956, i.e. **not** measurably more failure-rich than the fresh-noise
-`wm_full_oracle` (0.960): under the unit prior, `z` rarely reaches the failure regions.
+| `wm_full_x0_zprior` | `_s210…214` | pick_place + stack + unstack | X⁰, **z stored** | `full-xattn-branch-ot-100k` → `full_x0/` + `latent_action_full_x0_z8/` |
+
+### The `*_zprior` datasets
+
+Actions are drawn from a latent-action VAE's **sampling prior** and decoded to X⁰ through the
+frozen flow (`--latent-run`), with the sampled `z` stored in `actions/z` — the only shards
+carrying `z`. A z-native WM must read `actions/z` directly, **never** re-encode `x1` through the
+VAE posterior. In both, `actions/x0` is the **decoded X̂⁰** the flow actually executed, not a
+fresh `N(0, I)` draw.
+
+`wm_full_oracle_zprior` — `z ~ N(0, I)`, `(M, 2)` f32. Useful frac 0.953–0.956, i.e. **not**
+measurably more failure-rich than the fresh-noise `wm_full_oracle` (0.960): under the unit prior,
+`z` rarely reaches the failure regions.
+
+`wm_full_x0_zprior` — hybrid `z`, `(M, 8)` f32: a discrete code (one of 256, drawn from the
+empirical marginal) concatenated with 4 continuous dims `~ N(0, I)`. Useful frac 0.445–0.462
+against the fresh-noise `wm_full_x0`'s 0.76, so these shards *are* substantially failure-richer
+(173–174 of the 174 grounded actions still appear). Two properties matter before training on them:
+
+- **The action mix is skewed, not uniformly degraded.** Blind `z` sampling collapses toward
+  `pick_place`; the two multi-object actions nearly vanish. Ranges over the five shards:
+
+  | | none | pick_place | unstack | stack |
+  |---|---|---|---|---|
+  | `wm_full_x0` (fresh X⁰) | 24.4% | 52.2% | 12.0% | 11.5% |
+  | `wm_full_x0_zprior` | **53.8–55.5%** | 40.0–41.1% | **2.9–3.4%** | **1.3–1.8%** |
+
+- **The decoded X̂⁰ is not standard-normal — do not assume it is.** Every other dataset stores
+  noise with `mean|μ| ≈ 0.008` and `‖x‖² ≈ D = 2560`. Here the marginal is a different
+  distribution altogether (values are the range over the five shards, stored per file in the
+  `x0_normality` attr):
+
+  | | zprior | fresh-noise datasets |
+  |---|---|---|
+  | per-dim `mean|μ|` | **0.625–0.627** | ~0.008 |
+  | per-dim `std` | **0.463–0.465** | ~1.0 |
+  | `‖x‖²` | **3409–3422** (expect 2560) | ~2559 |
+  | `‖x‖²` spread | **536–541** (expect 72) | ~72 |
+  | dims rejecting normality | **98%** | — |
+  | dead-subset probe bal-acc | **0.577–0.592** | ~0.50 |
+
+  So each dimension is *narrower* than N(0,1) but carries a large mean offset, with heavy tails
+  (some dims reach `|μ| ≈ 5`). The dead-subset probe also rises above chance for the first time in
+  any of these datasets: unlike fresh noise, there **is** a linearly-separable "this noise does
+  nothing" region. The flow policy is being fed noise from well outside the shell it was trained
+  on, which is the likely mechanical cause of the ~55% no-op rate.
 
 (Seeds 105–124 of `wm_full_x0` also exist locally as image-free shards from a data-scaling
 study. All shards of a dataset are identical in format and interchangeable.)