neural: grounding refinement + all five Layer-1.5 figures

Grounding refinement (18 reps): forward-KL is the operative neural
collapse metric, not H or tail-survival. The RNN's smoothing keeps
spurious tail modes alive, so tail_truth_mass_alive is flat/non-monotone
in g and H stays ~0.8 of H*; only forward-KL falls monotonically (dry
2.08 -> g=0.2: 0.75, paired t up to 3.3). The sharp g* << 1 is an
exact-operator feature carried by the histogram bridge (0.047); the
trained RNN confirms the SIGN and softens the sharpness (half the KL gap
closes by g~0.04, but full recovery needs g~0.19). Blueprint 3.5's
directional claim holds; the pre-registered 95%-of-H*/tail falsifier is
not met because those are the wrong metrics for a smoothing model.

Robustness: a fully-degenerate RNN can emit only invalid codewords, so
measure_distribution now returns a terminal-collapse sentinel (fixation
on the dominant mode) instead of crashing a long sweep. Edge test added
(94 tests green).

Figures: plot_{bridge,collapse,grounding,architectures,recombination}.py,
each a pure function of its committed bundle, wired into `make figures`
(glob plot_*.py minus plot_E[1-6]/_*). bridge sits on the exact H_eq
curve (g*=0.047); recombination shows max-merge rising while mean-distill
stays flat; architectures shows the collapse/rescue signs across
histogram/GRU/MLP.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

figures/plot_collapse.py

@@ -0,0 +1,84 @@
+"""`collapse` figure — model collapse in REAL RNN weights, arrested by grounding (↔ E1/C1).
+
+The existence proof: a GRU trained each generation on the previous generation's own samples
+loses the rare tail and drifts from truth (forward-KL climbs), and even a little grounding
+arrests it. Forward-KL is the operative neural collapse metric (the RNN's smoothing keeps
+spurious tail support alive, so H barely moves — see the `grounding` finding).
+
+Four panels: (A) forward-KL trajectories (dry climbs, grounded suppressed); (B) H trajectories
+(barely moves — smoothing resists H-collapse); (C) stationary forward-KL vs g; (D) tail-item
+survival vs g. Reads only the committed bundle.
+
+Usage:  python figures/plot_collapse.py [results/collapse]
+"""
+
+from __future__ import annotations
+
+import sys
+from pathlib import Path
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+sys.path.insert(0, str(Path(__file__).parent))
+from _figlib import load_bundle, mean_ci, savefig  # noqa: E402
+
+sys.path.insert(0, str(Path(__file__).parents[1] / "src"))
+from knowledge.metrics import heterozygosity  # noqa: E402
+from neural.config import SyntheticCfg  # noqa: E402
+from neural.synthetic import make_mode_truth  # noqa: E402
+
+
+def main(results_dir: str = "results/collapse") -> None:
+    df, cfg = load_bundle(results_dir)
+    syn = SyntheticCfg(**cfg["synthetic"])
+    H_star = heterozygosity(make_mode_truth(syn).p_star)
+
+    g_values = sorted(df["g"].unique())
+    last = int(cfg["generations"] * 0.6)
+    stat = df[df["generation"] >= last]
+    colors = plt.cm.viridis(np.linspace(0, 0.85, len(g_values)))
+
+    fig, axes = plt.subplots(2, 2, figsize=(13, 9))
+
+    # Panel A: forward-KL trajectories (dry climbs, grounded suppressed).
+    ax = axes[0, 0]
+    for g, c in zip(g_values, colors):
+        s = df[df["g"] == g].groupby("generation")["forward_kl"].mean()
+        ax.plot(s.index, s.values, "-o", color=c, ms=3, label=f"g={g:g}")
+    ax.set(xlabel="generation", ylabel=r"forward-KL $D(p^*\Vert\hat p)$",
+           title="Collapse in weights: dry KL climbs, grounding holds it")
+    ax.legend(frameon=False, fontsize=9)
+
+    # Panel B: H trajectories (barely moves — smoothing resists H-collapse).
+    ax = axes[0, 1]
+    for g, c in zip(g_values, colors):
+        s = df[df["g"] == g].groupby("generation")["heterozygosity"].mean()
+        ax.plot(s.index, s.values, "-o", color=c, ms=3, label=f"g={g:g}")
+    ax.axhline(H_star, ls=":", color="gray", lw=1, label="$H^*$")
+    ax.set(xlabel="generation", ylabel="heterozygosity $H$",
+           title="H barely moves (RNN smoothing resists H-collapse)")
+    ax.legend(frameon=False, fontsize=9)
+
+    # Panel C: stationary forward-KL vs g.
+    ax = axes[1, 0]
+    kg, Km, Kci = mean_ci(stat, "g", "forward_kl")
+    ax.errorbar(kg, Km, yerr=Kci, fmt="o-", color="#1f77b4", capsize=3)
+    ax.set(xlabel="grounding fraction $g$", ylabel=r"stationary forward-KL",
+           title="Grounding lowers stationary divergence")
+
+    # Panel D: tail-item survival vs g.
+    ax = axes[1, 1]
+    tg, Tm, Tci = mean_ci(stat, "g", "tail_frac_alive")
+    ax.errorbar(tg, Tm, yerr=Tci, fmt="s-", color="#d62728", capsize=3)
+    ax.set(xlabel="grounding fraction $g$", ylabel="tail items alive",
+           title="Grounding lifts tail survival")
+
+    fig.suptitle("collapse — a trained GRU collapses under dry self-training; grounding arrests it "
+                 f"($K$={syn.K}, $n$={cfg['dynamics']['n']})", y=1.0, fontsize=13)
+    fig.tight_layout()
+    savefig(fig, results_dir, "collapse")
+
+
+if __name__ == "__main__":
+    main(*sys.argv[1:])