#!/usr/bin/env python3 """ MONISTIC FIELD THEORY: FLAGSHIP OVERVIEW FIGURE ================================================= Companion script for Paper 10 v2: "Monistic Field Theory" All panels use exact analytical formulas or hardcoded verified values. No Q-ball scanning or numerical solving — everything is deterministic. Author: Dale Wahl / MFT research programme, April 2026 """ import numpy as np import matplotlib; matplotlib.use('Agg') import matplotlib.pyplot as plt import matplotlib.patches as mpatches import os SCRIPT_DIR = os.path.dirname(os.path.abspath(__file__)) def outpath(fn): return os.path.join(SCRIPT_DIR, fn) # ═══════════════════════════════════════════════════════════════════ # EXACT MFT PARAMETERS (all derived, no fitting) # ═══════════════════════════════════════════════════════════════════ M2, LAM4, LAM6 = 1.0, 2.0, 0.5 DELTA = 1 + np.sqrt(2) PHI_B = np.sqrt(2 - np.sqrt(2)) # 0.7654 PHI_V = np.sqrt(2 + np.sqrt(2)) # 1.8478 PHI_CROSS = np.sqrt(2.0) # 1.4142 def V(phi): return 0.5*M2*phi**2 - 0.25*LAM4*phi**4 + (1/6.)*LAM6*phi**6 def Vpp(phi): return M2 - 3*LAM4*phi**2 + 5*LAM6*phi**4 V_at_b = V(PHI_B) # 1/(3δ) ≈ 0.138 V_at_v = V(PHI_V) # -δ/3 ≈ -0.805 Vpp_0 = Vpp(0) # = 1.0 Vpp_b = Vpp(PHI_B) # = -4/δ ≈ -1.657 Vpp_v = Vpp(PHI_V) # = 4δ ≈ 9.657 # Verified particle positions (from Paper 4) PARTICLES = { 'e': (0.022, 'green', 'o', 10), 'μ': (0.711, 'blue', 'o', 10), 'τ': (1.928, 'red', 'o', 10), 'W': (1.301, 'purple','s', 9), 'Z': (1.281, 'darkviolet','s', 9), 'H': (1.232, 'brown', 's', 9), } def main(): phi = np.linspace(0, 2.8, 1000) fig, axes = plt.subplots(2, 2, figsize=(16, 12)) fig.suptitle("Monistic Field Theory: A Theory of Spatial Contraction\n" r"One elastic medium, one derived potential $V_6(\varphi)$ with " r"$\lambda_4^2 = 8m_2\lambda_6$, silver ratio $\delta = 1+\sqrt{2}$", fontsize=13, fontweight='bold') # ═══════════════════════════════════════════════════════════════ # PANEL 1: The silver ratio potential with all particle positions # ═══════════════════════════════════════════════════════════════ ax = axes[0, 0] ax.plot(phi, V(phi), 'k-', lw=2.5) # Critical points ax.plot(0, V(0), 'go', ms=12, zorder=6) ax.plot(PHI_B, V_at_b, '^', color='orange', ms=12, zorder=6) ax.plot(PHI_V, V_at_v, 's', color='red', ms=12, zorder=6) # Vertical reference lines ax.axvline(PHI_B, color='orange', ls='--', lw=1, alpha=0.5) ax.axvline(PHI_V, color='red', ls='--', lw=1, alpha=0.5) ax.axvline(PHI_CROSS, color='green', ls=':', lw=1.5, alpha=0.7) # Particle positions for name, (pc, col, mk, ms) in PARTICLES.items(): ax.plot(pc, V(pc), mk, color=col, ms=ms, zorder=5) offset = 0.15 if name not in ['W', 'Z', 'H'] else -0.18 ax.annotate(name, (pc, V(pc)), textcoords="offset points", xytext=(0, 12 if offset > 0 else -14), ha='center', fontsize=8, fontweight='bold', color=col) # Annotations for silver ratio values ax.annotate(f'$\\varphi_b = {PHI_B:.3f}$\n$V = 1/(3\\delta) = {V_at_b:.3f}$', xy=(PHI_B, V_at_b), xytext=(0.15, 0.7), fontsize=7, color='orange', arrowprops=dict(arrowstyle='->', color='orange', lw=0.8)) ax.annotate(f'$\\varphi_v = {PHI_V:.3f}$\n$V = -\\delta/3 = {V_at_v:.3f}$', xy=(PHI_V, V_at_v), xytext=(2.2, -0.3), fontsize=7, color='red', arrowprops=dict(arrowstyle='->', color='red', lw=0.8)) ax.annotate(f'$\\sqrt{{2}} = \\delta-1$\n(crossing)', xy=(PHI_CROSS, V(PHI_CROSS)), xytext=(1.7, 1.5), fontsize=7, color='green', arrowprops=dict(arrowstyle='->', color='green', lw=0.8)) # Ratio annotation ax.annotate('', xy=(PHI_V, -1.0), xytext=(PHI_B, -1.0), arrowprops=dict(arrowstyle='<->', color='navy', lw=1.5)) ax.text((PHI_B+PHI_V)/2, -1.08, f'$\\varphi_v/\\varphi_b = \\delta = {DELTA:.3f}$', ha='center', fontsize=8, color='navy', fontweight='bold') ax.set_xlabel('$\\varphi$ (contraction field)', fontsize=10) ax.set_ylabel('$V_6(\\varphi)$', fontsize=10) ax.set_title('The silver ratio potential\nwith all particle positions', fontsize=11) ax.set_ylim(-1.3, 2.5); ax.set_xlim(-0.05, 2.75) ax.grid(True, alpha=0.2) # ═══════════════════════════════════════════════════════════════ # PANEL 2: Stiffness V''(φ) showing the three regimes # ═══════════════════════════════════════════════════════════════ ax = axes[0, 1] ax.plot(phi, Vpp(phi), 'b-', lw=2.5) ax.axhline(0, color='black', lw=0.5) # Mark the three critical stiffness values ax.plot(0, Vpp_0, 'go', ms=12, zorder=6) ax.plot(PHI_B, Vpp_b, '^', color='orange', ms=12, zorder=6) ax.plot(PHI_V, Vpp_v, 's', color='red', ms=12, zorder=6) # Shade the three regimes ax.axvspan(0, PHI_B, alpha=0.08, color='green', label='Linear vacuum') ax.axvspan(PHI_B, PHI_V, alpha=0.08, color='orange', label='Barrier region') ax.axvspan(PHI_V, 2.8, alpha=0.08, color='red', label='Nonlinear vacuum') # Stiffness labels ax.annotate(f"$V''(0) = {Vpp_0:.1f}$\n(baseline)", xy=(0, Vpp_0), xytext=(0.3, 3.0), fontsize=8, color='green', arrowprops=dict(arrowstyle='->', color='green', lw=0.8)) ax.annotate(f"$V''(\\varphi_b) = -4/\\delta$\n$= {Vpp_b:.2f}$\n(unstable)", xy=(PHI_B, Vpp_b), xytext=(0.2, -5), fontsize=8, color='orange', arrowprops=dict(arrowstyle='->', color='orange', lw=0.8)) ax.annotate(f"$V''(\\varphi_v) = 4\\delta$\n$= {Vpp_v:.2f}$\n(9.66× stiffer)", xy=(PHI_V, Vpp_v), xytext=(2.1, 6), fontsize=8, color='red', arrowprops=dict(arrowstyle='->', color='red', lw=0.8)) # The 4δ ratio ax.annotate('', xy=(2.55, Vpp_v), xytext=(2.55, Vpp_0), arrowprops=dict(arrowstyle='<->', color='navy', lw=1.5)) ax.text(2.65, (Vpp_v+Vpp_0)/2, f'$4\\delta$\n$≈ 9.66×$', fontsize=9, color='navy', fontweight='bold', va='center') ax.set_xlabel('$\\varphi$ (contraction field)', fontsize=10) ax.set_ylabel("$V''(\\varphi)$ (stiffness)", fontsize=10) ax.set_title('Medium stiffness across three regimes\n' '(electron → barrier → tau/bosons)', fontsize=11) ax.set_ylim(-7, 14); ax.set_xlim(-0.05, 2.8) ax.legend(fontsize=8, loc='lower right') ax.grid(True, alpha=0.2) # ═══════════════════════════════════════════════════════════════ # PANEL 3: Four physical regimes (schematic) # ═══════════════════════════════════════════════════════════════ ax = axes[1, 0] ax.set_xlim(0, 10); ax.set_ylim(0, 10) ax.axis('off') ax.set_title('Four physical regimes of MFT\n(same field equations, different limits)', fontsize=11) regimes = [ (1.5, 8.0, 'Dense, Weak-Field\n(Solar System)', 'steelblue', '• φ screened, short-ranged\n' '• Reduces to GR + corrections\n' '• ω_BD > 40,000 (Cassini)\n' '• PPN parameters match GR'), (6.5, 8.0, 'Low-Density, Galactic', 'forestgreen', '• φ unscreened across kpc\n' '• Nonlinear BVP for halos\n' '• Σχ²/dof = 1.17 (6 galaxies)\n' '• No dark matter needed'), (1.5, 3.5, 'Black-Hole Limit', 'darkred', '• φ → φ_v (elastic ceiling)\n' '• V″(φ_v) = 4δ bounds density\n' '• Non-singular interiors\n' '• Finite curvature everywhere'), (6.5, 3.5, 'Cosmological (Voids)', 'darkorange', '• Low-density void evolution\n' '• Effective Hubble law from φ\n' '• Acceleration without Λ\n' '• Dielectric → Hubble tension?'), ] for x, y, title, color, desc in regimes: box = mpatches.FancyBboxPatch((x-2.0, y-2.0), 4.0, 3.2, boxstyle="round,pad=0.15", facecolor=color, alpha=0.12, edgecolor=color, lw=2) ax.add_patch(box) ax.text(x, y+0.8, title, ha='center', va='center', fontsize=10, fontweight='bold', color=color) ax.text(x, y-0.5, desc, ha='center', va='center', fontsize=7.5, color='black', family='monospace') # Central label ax.text(4.0, 5.75, 'Same action\nSame φ\nSame V₆(φ)', ha='center', va='center', fontsize=10, fontweight='bold', color='black', style='italic', bbox=dict(boxstyle='round', facecolor='lightyellow', edgecolor='gray', alpha=0.9)) # ═══════════════════════════════════════════════════════════════ # PANEL 4: The complete derivation chain # ═══════════════════════════════════════════════════════════════ ax = axes[1, 1] ax.set_xlim(0, 10); ax.set_ylim(0, 10) ax.axis('off') ax.set_title('The MFT derivation chain (16 papers)\n(each step is a theorem — zero free parameters in the potential)', fontsize=11) steps = [ (0, 'MFT Action', 'Scalar-tensor on 3D slice', 'Paper 0'), (1, 'K₆>0, K₂>0, K₄<0', "Derrick's theorem", 'Paper 1'), (2, 'λ₄² = 8m₂λ₆', 'Back-Reaction Theorem', 'Paper 2'), (3, 'Exactly 3 families', 'Morse index n−1', 'Paper 3'), (4, 'All particle masses', 'Q-ball equation', 'Paper 4'), (5, 'Rotation curves', 'Nonlinear BVP', 'Paper 5'), (6, 'Spin-½ (14× gap)', 'Emergent Lorentz + FR', 'Paper 6'), (7, 'Confinement', 'Elastic topology', 'Paper 7'), (8, 'Microphysics synthesis', 'Skyrme + neutral solitons', 'Paper 8'), (9, 'Flagship (this paper)', 'Complete foundations', 'Paper 9'), (10,'Quantum completion', 'Hamiltonian + Fock space', 'Paper 10'), (11,'Propagators + vertices', 'Linearised (ω,k) space', 'Paper 11'), (12,'Cosmology without Λ', 'Void expansion + H₀', 'Paper 12'), (13,'Compact objects + PPN', 'Yukawa, saturation', 'Paper 13'), (14,'EM form factor + g=2', 'F_MFT = F_QED + O(10⁻⁴⁵)', 'Paper 14'), (15,'3D finiteness', 'Q-ball separation + [λ₆]=0', 'Paper 15'), ] n = len(steps) for i, (idx, result, method, paper) in enumerate(steps): y = 9.5 - i * 0.58 # Step box — color by grouping: # Blue = foundations (P0–P2); Green = predictions (P3–P5); # Red = microphysics (P6–P8); Orange = quantum + astro (P9–P15) color = 'steelblue' if i < 3 else ('forestgreen' if i < 6 else ('darkred' if i < 9 else 'darkorange')) ax.add_patch(mpatches.FancyBboxPatch((0.2, y-0.21), 3.2, 0.42, boxstyle="round,pad=0.06", facecolor=color, alpha=0.15, edgecolor=color, lw=1.5)) ax.text(1.8, y, result, ha='center', va='center', fontsize=7, fontweight='bold', color=color) # Arrow if i < n-1: ax.annotate('', xy=(1.8, y-0.26), xytext=(1.8, y-0.32), arrowprops=dict(arrowstyle='->', color='gray', lw=1)) # Method ax.text(5.0, y, method, ha='left', va='center', fontsize=7, color='gray') # Paper ax.text(8.5, y, paper, ha='left', va='center', fontsize=7, color='black', style='italic') # Legend ax.text(0.2, 0.3, 'Blue = foundations Green = predictions Red = microphysics Orange = quantum + astro', fontsize=7, color='gray') plt.tight_layout(rect=[0, 0, 1, 0.91]) out = outpath('mft_flagship.png') plt.savefig(out, dpi=150, bbox_inches='tight') print(f"Figure saved: {out}") print("All panels use exact analytical formulas — zero numerical scanning.") if __name__ == '__main__': main()