Pair the steer CI against base, save the answer primitive, add a manipulation check

The absolute WVS coordinate carries +-0.07 of item-set variance on a 12-item
battery, so the steer is now reported as a paired difference on the same items.
Per-dose psamples are saved, so every interval is post-processing.

The manipulation check exists because a flat map cannot be read on its own: a
vector that does nothing and a vector that culture does not respond to look the
same. Qwen3-0.6B: per-item changes are large (sd 0.18-0.38) but their signs are
coin flips (7/12 up), and random behaves the same.

Co-Authored-By: Claude <288921227+claudypoo@users.noreply.github.com>

scripts/plot_wvs_steer.py

@@ -104,8 +104,9 @@ def main() -> None:
             far = max(side, key=lambda d: abs(d["mult"]))
             worst, loo_len = loo_worst(far, r["doses"][0], resolved)
             rows.append([r["method"], r["seed"], f"{r['calibrated_C']:+.3f}", f"{far['mult']:+.1f}",
-                         f"{far['x'] - base['x']:+.4f}", f"{far['y'] - base['y']:+.4f}",
-                         f"{np.hypot(far['x'] - base['x'], far['y'] - base['y']):.4f}",
+                         f"{far['dx']:+.4f}+-{1.96 * far['dx_se']:.3f}",
+                         f"{far['dy']:+.4f}+-{1.96 * far['dy_se']:.3f}",
+                         f"{np.hypot(far['dx'], far['dy']):.4f}",
                          f"{loo_len:.4f}", worst or "-", f"{far['mean_pmass']:.3f}"])
 
     # the reach of random directions at the same iso-KL dose: anything inside this has shown nothing.
@@ -125,8 +126,11 @@ def main() -> None:
 
     rows.sort(key=lambda r: -float(r[6]))
     print(tabulate(rows, tablefmt="pipe", headers=[
-        "method", "seed", "C", "dose", "dx", "dy", "|move|", "|move| less worst item",
-        "worst item", "pmass"]))
+        "method", "seed", "C", "dose", "dx (95%)", "dy (95%)", "|move|",
+        "|move| less worst item", "worst item", "pmass"]))
+    print("\ndx/dy intervals are PAIRED against base on the same items. The absolute coordinate is\n"
+          "much less certain (+-0.07 on X for a 12-item battery); that uncertainty is shared by base\n"
+          "and dose, so it limits where the model sits among societies, not how far the steer moved it.")
     logger.info(f"wrote {args.out} ({dropped} doses dropped below pmass {args.min_pmass})")