Layer 1 complete: E3-E6 + E2 analysis add-ons

Finishes the Layer 1 analytical core. All six experiments run with honest,
publication-quality figures; 71 tests green.

- E3 region-matched grounding: `grounding.exercised` knob + per-region tail
  survival. Matched holds the exercised region's tail (0.49) where uniform
  spreads thin and lets it collapse (0.07).
- E4 multi-teacher recombination: `run_coverage` runner. Union coverage matches
  U(K_T,rho,q) exactly. Finding: mean-mixture distillation shows NO surviving
  benefit (a conservation law — 1/K_T dilution cancels the union gain); a
  union-preserving max-merge (M2N2-style) does. E4 reports both operators.
- E5 QD vs greedy: greedy drives fixation (H~0.01); QD holds H at 0.48-0.88,
  rising with the novelty exponent.
- E6 re-mint gate: `arm` multi-override sweep. Re-minting a collapsed lineage
  locks in divergence of KL-to-original; gating on diversity prevents it.
- E2 analysis add-ons (from the companion work order, numbers verified): new
  analysis.py (reduce_to_stationary, critical_grounding with bootstrap CI ->
  g*=0.048, 95% CI [0.047,0.050]); tail_band_metrics + per-band logging; the
  E2 figure rebuilt as a 2x2 (defined g*+CI, g=0 flagged as a finite-time
  artifact, tail item-vs-mass, per-rarity-band panel). Uses truth-mass-weighted
  tail coverage rather than the raw (martingale) tail_mass.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/knowledge/metrics.py

@@ -79,6 +79,42 @@ def support_size(p: np.ndarray, eps: float) -> int:
     return int(np.sum(p > eps))
 
 
+def tail_band_metrics(p: np.ndarray, p_star: np.ndarray, tail_mask: np.ndarray,
+                      n_bands: int = 4, alive_eps: float = 1e-9):
+    """Stratify the tail into ``n_bands`` equal-count rarity bands (band 0 = rarest).
+
+    Makes the per-item survival threshold ``m·p*_i ≳ 1`` (blueprint prediction 4) visible
+    band-wise: deeper (rarer) bands sit strictly below shallower ones and the gap narrows
+    as grounding rises. Both returned arrays are bounded in [0, 1]; single-run values are
+    noisy, so average over replicates before plotting.
+
+    Args:
+        p (np.ndarray): Current distribution.
+        p_star (np.ndarray): True distribution.
+        tail_mask (np.ndarray): Boolean tail mask.
+        n_bands (int): Number of equal-count rarity bands.
+        alive_eps (float): An item is "alive" if ``p_i > alive_eps``.
+
+    Returns:
+        tuple[np.ndarray, np.ndarray]: ``frac_alive[b]`` (fraction of band-b items alive)
+        and ``truth_mass_alive[b]`` (share of band-b's TRUE mass carried by alive items),
+        each length ``n_bands``.
+    """
+    p = np.asarray(p, dtype=float)
+    p_star = np.asarray(p_star, dtype=float)
+    idx = np.where(np.asarray(tail_mask, dtype=bool))[0]
+    order = idx[np.argsort(p_star[idx])]           # rarest first
+    bands = np.array_split(order, n_bands)
+    frac_alive = np.empty(n_bands)
+    truth_mass_alive = np.empty(n_bands)
+    for b, items in enumerate(bands):
+        alive = p[items] > alive_eps
+        frac_alive[b] = alive.mean()
+        ps = p_star[items]
+        truth_mass_alive[b] = ps[alive].sum() / ps.sum() if ps.sum() > 0 else np.nan
+    return frac_alive, truth_mass_alive
+
+
 def per_region(func, p: np.ndarray, regions: np.ndarray, *args) -> dict[int, float]:
     """Apply a metric independently to each region's sub-vector.