#!/usr/bin/env python3 """ plot_widening_ladder.py — the "L0 reactive-widening ladder". Diagnostic for PPDF-16 (the DIS-only degeneracy verdict). During the full-DIS L0 closure gate, UltraNest's reactive strategy kept judging the effective sample size insufficient and doubling the live-point population — 300 → 600 → 1200 → 2400 — burning iterations at each level without ever converging. That runaway escalation IS the confirmation of a structurally under-constrained (degenerate) model: on a bowl-shaped posterior the sampler settles; on a posterior riddled with flat directions it never does. Data (hardcoded from the L0 log; see context/RESULTS_LEDGER.md, PPDF-16): live points N vs cumulative iterations at each widening round N=300 -> 15100 N=600 -> 18500 N=1200 -> 43000 N=2400 -> 56300 Output: site/assets/img/ppdf16_widening_ladder.png """ import os import matplotlib matplotlib.use("Agg") import matplotlib.pyplot as plt from matplotlib.ticker import FuncFormatter # ---- site palette (assets/site.css :root) ------------------------------- TEAL = "#0e7c7b" TEAL_DARK = "#0e5453" ORANGE = "#d96c2c" INK = "#16222e" BODY = "#37424e" MUTED = "#4a5866" FAINT = "#8a94a0" BG = "#fdfcfa" PANEL = "#f2efe9" LINE = "#d5cfc2" # ---- data (widening ladder) --------------------------------------------- live_points = [300, 600, 1200, 2400] # N at each reactive-widening round cum_iters = [15100, 18500, 43000, 56300] # cumulative UltraNest iterations # iterations spent *at* each level = successive differences of the cumulative iters_at_level = [cum_iters[0]] + [ cum_iters[i] - cum_iters[i - 1] for i in range(1, len(cum_iters)) ] # ---- figure ------------------------------------------------------------- plt.rcParams.update( { "font.family": "DejaVu Sans", "font.size": 12, "axes.edgecolor": LINE, "axes.linewidth": 1.0, "figure.facecolor": BG, "axes.facecolor": BG, } ) fig, ax = plt.subplots(figsize=(9.6, 5.6)) x = list(range(len(live_points))) labels = [f"N = {n}" for n in live_points] # bar per widening round, height = cumulative iterations reached at that round. # colour deepens toward orange as the escalation runs away (never converges). bar_colors = [TEAL, TEAL_DARK, "#a15a1f", ORANGE] bars = ax.bar( x, cum_iters, width=0.62, color=bar_colors, edgecolor="white", linewidth=1.5, zorder=3, ) # stepped "escalation" line tracing the top of the ladder (post step: the # population doubling happens between rounds). ax.step( [xi + 0.5 for xi in [-1] + x], [cum_iters[0]] + cum_iters, where="pre", color=INK, linewidth=1.6, linestyle="--", alpha=0.55, zorder=4, ) # annotate each bar: live-point count (bottom) + iterations spent at that level for xi, n, cum, spent, col in zip(x, live_points, cum_iters, iters_at_level, bar_colors): # cumulative total at top of the bar ax.text( xi, cum + 1400, f"{cum:,}\niterations", ha="center", va="bottom", fontsize=11.5, color=INK, fontweight="bold", linespacing=1.15, ) # "+spent this round" inside the bar, near the top if xi > 0: ax.text( xi, cum - 3200, f"+{spent:,}\nthis round", ha="center", va="top", fontsize=10, color="white", linespacing=1.1, ) # the doubling arrows between rounds — the "reactive widening" itself. # label sits just below the arrow midpoint to stay clear of the bar-top totals. for i in range(len(x) - 1): mid_y = (cum_iters[i] + cum_iters[i + 1]) / 2 ax.annotate( "live points\ndoubled", xy=(x[i] + 0.5, mid_y - 4200), ha="center", va="top", fontsize=9, color=ORANGE, fontweight="bold", linespacing=1.05, ) ax.annotate( "", xy=(x[i + 1] - 0.30, cum_iters[i + 1] * 0.985), xytext=(x[i] + 0.30, cum_iters[i] * 1.02), arrowprops=dict(arrowstyle="-|>", color=ORANGE, lw=1.6, alpha=0.9), zorder=5, ) # "killed by decision — never converged" flag at the final round. # offset left so the arrow doesn't cross the bar-top total. ax.annotate( "killed by decision\n(never converged)", xy=(x[-1] - 0.28, cum_iters[-1] * 0.995), xytext=(x[-1] - 0.62, cum_iters[-1] + 11500), ha="center", va="bottom", fontsize=10.5, color=ORANGE, fontweight="bold", linespacing=1.15, arrowprops=dict(arrowstyle="-|>", color=ORANGE, lw=1.8), ) # axes cosmetics ax.set_xticks(x) ax.set_xticklabels(labels, fontsize=13, color=INK, fontweight="bold") ax.set_xlim(-0.75, len(x) - 0.25) ax.set_ylim(0, cum_iters[-1] * 1.40) ax.set_ylabel("cumulative UltraNest iterations", fontsize=12.5, color=MUTED) ax.set_xlabel("reactive-widening round → live-point population", fontsize=12.5, color=MUTED) ax.yaxis.set_major_formatter(FuncFormatter(lambda v, _: f"{int(v/1000)}k")) ax.tick_params(axis="y", colors=MUTED, labelsize=11) ax.tick_params(axis="x", length=0) for spine in ("top", "right"): ax.spines[spine].set_visible(False) ax.grid(axis="y", color=LINE, linewidth=0.7, alpha=0.55, zorder=0) ax.set_axisbelow(True) ax.set_title( "L0 discriminator: reactive widening never converged (zero-noise closure)", fontsize=14.5, color=INK, fontweight="bold", pad=16, ) # subtitle / reading aid fig.text( 0.5, 0.005, "Full-DIS 52-parameter MSHT fit · escalating live points is the tell of a degenerate, flat-direction posterior — not a sampler setting to tune.", ha="center", va="bottom", fontsize=9.5, color=FAINT, ) fig.tight_layout(rect=(0, 0.03, 1, 1)) # ---- save --------------------------------------------------------------- out_dir = os.path.join( os.path.dirname(os.path.dirname(os.path.abspath(__file__))), "site", "assets", "img", ) os.makedirs(out_dir, exist_ok=True) out_path = os.path.join(out_dir, "ppdf16_widening_ladder.png") fig.savefig(out_path, dpi=150, facecolor=BG, bbox_inches="tight") print(f"wrote {out_path}")