Figure3_Stability_Hierarchy.txt

Figure3_Stability_Hierarchy 

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
from mpl_toolkits.axes_grid1.inset_locator import inset_axes
import os
from pathlib import Path

# --- STYLE SETTINGS ---
plt.rcParams['font.family'] = 'serif'
plt.rcParams['font.serif'] = ['Times New Roman', 'Times', 'DejaVu Serif', 'serif']
plt.rcParams['font.size'] = 12
plt.rcParams['axes.linewidth'] = 1.2
plt.rcParams['xtick.direction'] = 'in'
plt.rcParams['ytick.direction'] = 'in'
plt.rcParams['mathtext.fontset'] = 'cm'
plt.rcParams['svg.fonttype'] = 'none'

# ==========================================
# FIGURE 3: THE STABILITY HIERARCHY
# ==========================================
fig3, ax = plt.subplots(figsize=(14, 14))

# 1. The Critical Line (Vacuum)
line_diag = np.linspace(-35, 30, 100)
ax.plot(line_diag, line_diag, 'k-', alpha=0.2)
ax.fill_between(line_diag, line_diag-0.5, line_diag+0.5, color='gray', alpha=0.1)

# ==========================================
# 2. THE DATASET
# ==========================================

# A. VACUUM SCALES (Red Diamonds)
vacuum = {
    'Planck Scale': (28, 28),
    'GUT Scale': (25, 25),
    'Electroweak': (11.4, 11.4),
    'QCD Scale': (8.3, 8.3),
    'Dark Energy': (-32.8, -32.8)
}

# B. LEPTONS (Blue Circles)
leptons = {
    'Neutrino': (-1.3, -25.0),
    'Electron': (5.7, -15.0),
    'Muon': (8.02, -9.5),
    'Tau': (9.25, -2.65),
}

# C. BARYONS (Green Squares)
baryons = {
    'Proton': (9.0, -25.0),
    'Neutron': (9.0, -18.8),
    'Lambda': (9.05, -9.6),
    'Sigma+': (9.07, -10.1),
    'Xi': (9.12, -9.5),
    'Omega-': (9.22, -9.9),
}

# D. MESONS (Orange Triangles)
mesons = {
    'Pion (+/-)': (8.15, -7.6),
    'Pion (0)': (8.13, 0.9),
    'Kaon': (8.69, -7.9),
    'Rho': (8.88, 8.17),
    'Omega Meson': (8.89, 6.9),
    'Phi': (9.01, 6.6),
    'J/Psi': (9.49, 4.97),
    'Upsilon': (9.97, 4.73),
    'B-Meson': (9.72, -3.8),
    'D-Meson': (9.27, -4.1)
}

# E. BOSONS (Purple Stars)
bosons = {
    'W Boson': (10.9, 9.32),
    'Z Boson': (10.96, 9.39),
    'Higgs': (11.09, 6.6),
    'Top Quark': (11.19, 9.15),
    'Delta Baryon': (9.09, 8.07)
}

# F. COSMIC OUTLIERS (Cyan Hexagons)
outliers = {
    'OMG': (20.5, -13.0),
    'Amaterasu': (20.38, -13.0)
}

# ==========================================
# 3. PLOTTING LOOP
# ==========================================

def plot_group(data, color, marker, label):
    for name, (x, y) in data.items():
        # Drop Line
        ax.plot([x, x], [x, y], color=color, linestyle='--', linewidth=0.8, alpha=0.3, zorder=1)
        # Point
        ax.scatter(x, y, c=color, marker=marker, s=110, edgecolors='k', linewidth=0.5, zorder=5)

        # LABELING
        offset_x, offset_y = 0.5, 0.5
        ha, va = 'left', 'bottom'

        # Manual Nudges
        if name == 'Pion (+/-)': offset_x, offset_y = -3, 2; ha='right'
        if name == 'Pion (0)': offset_x, offset_y = -3, -1; ha='right'
        if name == 'Kaon': offset_x, offset_y = 2, -1
        if name == 'Rho': offset_x, offset_y = -3, 2; ha='right'
        if name == 'Omega Meson': offset_x, offset_y = 2, 0
        if name == 'Phi': offset_x, offset_y = 2, -1.5
        if name == 'Delta Baryon': offset_x, offset_y = -4, 0; ha='right'
        if name == 'Xi': offset_x, offset_y = 2, 0
        if name == 'Omega-': offset_x, offset_y = 2, -1
        if name == 'Lambda': offset_x, offset_y = -3, -1; ha='right'
        if name == 'Sigma+': offset_x, offset_y = -3, -2.5; ha='right'
        if name == 'Higgs': offset_x, offset_y = 3, 0
        if name == 'Top Quark': offset_x, offset_y = 3, 1.5
        if name == 'Z Boson': offset_x, offset_y = -3, 2; ha='right'
        if name == 'W Boson': offset_x, offset_y = -3, 3.5; ha='right'
        if name == 'Planck Scale': offset_x, offset_y = -2, 0; ha='right'
        if name == 'Dark Energy': offset_x, offset_y = 2, 0; ha='left'
        if name == 'OMG': continue
        if name == 'Amaterasu': continue

        # DRAW LINE AND LABEL
        ax.annotate(name,
                    xy=(x, y), xycoords='data',
                    xytext=(x + offset_x, y + offset_y), textcoords='data',
                    arrowprops=dict(arrowstyle='-', color=color, lw=0.6),
                    fontsize=11, color=color, ha=ha, va=va,
                    fontweight='bold' if 'Scale' in name else 'normal')

    return Line2D([0], [0], marker=marker, color='w', label=label,
                  markerfacecolor=color, markersize=10, markeredgecolor='k')

# Execute
h1 = plot_group(vacuum, '#D81B60', 'D', 'Vacuum Scale')
h2 = plot_group(bosons, '#9C27B0', '*', 'Force Carriers')
h3 = plot_group(mesons, '#FF9800', '^', 'Mesons')
h4 = plot_group(baryons, '#4CAF50', 's', 'Baryons')
h5 = plot_group(leptons, '#2196F3', 'o', 'Leptons')
h6 = plot_group(outliers, '#00BCD4', 'h', 'UHECR Cluster')

# ==========================================
# 4. MANUAL ANNOTATIONS
# ==========================================

ax.annotate('UHECR Cluster\n(OMG & Amaterasu)', xy=(20.4, -13.0), xytext=(20.4, -8),
            color='#00BCD4', ha='center', fontweight='bold', fontsize=12,
            arrowprops=dict(arrowstyle='-', color='#00BCD4', lw=0.6))

# ==========================================
# 5. LEGEND (THE FIX)
# ==========================================

# Standard, Robust Proxy Artist
# We use a Dark Gray dashed line to represent "The dashed lines on the plot"
h_precip = Line2D([0], [0], color='gray', linewidth=2, linestyle='--', label='Thermodynamic Precipitation')

handles = [h1, h2, h3, h4, h5, h6, h_precip]

ax.legend(handles=handles, loc='upper left', frameon=True, fontsize=12, framealpha=0.95)

# ==========================================
# 6. FORMATTING
# ==========================================
ax.set_xlim(-35, 30)
ax.set_ylim(-35, 30)
ax.set_xlabel(r'Log$_{10}$ Energy Scale $\omega$ [eV]', fontsize=16)
ax.set_ylabel(r'Log$_{10}$ Damping Scale $\Gamma$ [eV]', fontsize=16)
ax.set_title('The Stability Hierarchy', fontsize=20, fontweight='bold', pad=20)

# Histogram
ax_ins = inset_axes(ax, width="25%", height="20%", loc='lower right', borderpad=3)
np.random.seed(42)
data_peak = np.random.normal(0, 0.3, 1000)
ax_ins.hist(data_peak, bins=30, color='gray', alpha=0.6)
ax_ins.axvline(0, color='#D81B60', lw=2)
ax_ins.set_title('Vacuum Variance', fontsize=11)
ax_ins.set_xticks([])
ax_ins.set_yticks([])

# Save
downloads_path = str(Path.home() / "Downloads")
if not os.path.exists(downloads_path): downloads_path = os.getcwd()
plt.savef