Giorgio Gilestro
a6eb9b7512
Scaffold plus the Layer 1 analytical core and the first two experiments. - knowledge/: truth, metrics, teachers (2.7.1 shared-switch construction), step, lineage, experiment, config, seeding (imported as `knowledge`). - Validation spine green: neutral decay (Pred 1), fixation (Pred 2), exact mutation-drift equilibrium (Pred 3), union coverage (Pred 5). 68 tests pass. - E1 reproduces tail-first collapse. E2 delivers the headline: a grounding phase boundary g* << 1, with stationary H tracking the exact H_eq closed form (g=0.005 -> 68% of truth diversity; g=0.05 -> 96%). - Reproducibility: uv venv from a hash-pinned uv.lock is the source of truth; every run writes results.parquet + resolved_config.yaml + manifest.json (lib versions, git commit, sha256). Figures and manifests tracked; the large regenerable parquet is gitignored. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
85 lines
3.6 KiB
Python
85 lines
3.6 KiB
Python
"""E2 figure: the grounding phase boundary (headline).
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Shows that a critical grounding fraction g* << 1 separates collapse from a healthy
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plateau: H trajectories (g=0 slides to 0, g>0 plateau), and stationary H / tail mass vs
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g with the exact analytic H_eq overlaid. Usage: python figures/plot_E2.py [results/E2]
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"""
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from __future__ import annotations
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import sys
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from pathlib import Path
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import matplotlib.pyplot as plt
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import numpy as np
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sys.path.insert(0, str(Path(__file__).parent))
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from _figlib import load_bundle, mean_ci, savefig # noqa: E402
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sys.path.insert(0, str(Path(__file__).parents[1] / "src"))
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from knowledge.metrics import heterozygosity # noqa: E402
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from knowledge.truth import make_true_distribution # noqa: E402
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def main(results_dir: str = "results/E2") -> None:
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df, cfg = load_bundle(results_dir)
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n = cfg["dynamics"]["n"]
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K, zs = cfg["truth"]["K"], cfg["truth"]["zipf_s"]
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td = make_true_distribution(K, 1, "zipf", cfg["truth"]["tail_frac"], zs, 0,
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tail_threshold=cfg["truth"]["tail_threshold"])
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H_star = heterozygosity(td.p_star)
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def H_eq(m): # exact stationary heterozygosity (blueprint 2.4-3)
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m = np.asarray(m, dtype=float)
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return np.where(m <= 0, 0.0, H_star * m * (2 * n + m - 1) / (n + 2 * n * m + m * m))
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g_values = sorted(df["g"].unique())
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last = int(cfg["generations"] * 0.8) # stationary window: final 20% of generations
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fig, axes = plt.subplots(1, 3, figsize=(15, 4.2))
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# Panel 1: H trajectories, one line per g
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ax = axes[0]
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colors = plt.cm.viridis(np.linspace(0, 0.9, len(g_values)))
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for g, c in zip(g_values, colors):
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sub = df[df["g"] == g].groupby("generation")["heterozygosity"].mean()
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ax.plot(sub.index, sub.values, color=c, label=f"g={g:g}")
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ax.axhline(H_star, ls=":", color="gray", lw=1)
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ax.set(xlabel="generation", ylabel="heterozygosity $H$",
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title="Trajectories: g=0 collapses, g>0 plateau")
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ax.legend(frameon=False, fontsize=8, ncol=2)
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# Panel 2: stationary H vs g, with exact H_eq overlay
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stat = df[df["generation"] >= last]
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gg, Hm, Hci = mean_ci(stat, "g", "heterozygosity")
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m_of_g = stat.groupby("g")["m"].first().to_numpy()
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ax = axes[1]
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ax.errorbar(gg, Hm, yerr=Hci, fmt="o", color="#1f77b4", capsize=3,
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label="simulation (stationary)", zorder=3)
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m_grid = np.linspace(0, m_of_g.max(), 400)
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g_grid = m_grid / (n + m_grid)
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ax.plot(g_grid, H_eq(m_grid), "k--", label=r"exact $H_{eq}$", zorder=2)
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ax.axhline(H_star, ls=":", color="gray", lw=1, label="$H^*$ (truth)")
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ax.set(xlabel="grounding fraction $g=m/(n+m)$", ylabel="stationary $H$",
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title=r"Phase boundary: $g^\star \ll 1$")
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ax.legend(frameon=False, fontsize=9)
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# Panel 3: stationary fraction of TAIL ITEMS still alive vs g. (Aggregate tail *mass*
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# is a drift martingale and near-constant, so it is a poor indicator; the fraction of
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# rare items kept alive is the honest, monotone measure of how much tail grounding
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# rescues.) Tail-item survival rises steeply with g even where H is already saturated.
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tg, Tm, Tci = mean_ci(stat, "g", "tail_frac_alive")
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ax = axes[2]
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ax.errorbar(tg, Tm, yerr=Tci, fmt="s", color="#d62728", capsize=3)
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ax.set(xlabel="grounding fraction $g$",
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ylabel="fraction of tail items alive",
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title="Grounding keeps rare items alive")
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fig.suptitle("E2 — a critical grounding ratio $g^\\star \\ll 1$ separates ratchet "
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"from collapse", y=1.02)
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fig.tight_layout()
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savefig(fig, results_dir, "E2")
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if __name__ == "__main__":
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main(*sys.argv[1:])
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