Self-Regulated Galaxy Stability Model - Torque Cut by Waveguide Phase Flip: Equiangular Spiral-Waveguide Formalism

Abstract This work presents an alternative framework that reproduces the observed flat bar profile, longevity of spiral arms, and R_CR/R_bar clustering without invoking a dark matter halo as a stabilizing agent. Rather than contradicting the standard picture, it provides a concrete geometric implementation for what has been phenomenologically described as a density wave: the maintenance mechanism is identified as a waveguide phase-flip and torque cut at r_cut. We apply the waveguide function T_w(r,θ)=e^(-k·r)·e^(±jψ). At the isogonal branching point where the rotating bar ends and spiral arms begin, phase ψ flips by 180°, high wave energy surges, torque connection is cut, forming cut-off radius r_cut. This is the critical jump Vcrit≈180km/s observed in PHANGS (38 galaxies) and S4G (40 galaxies) catalogs, and Hoag's Object (PGC 54559) is the extreme manifestation where this cut-off is most prominently visualized. All 6 figures are consistently explained by one formalism: Fig1 Force cancellation at r_c~6.0kpc (τ_eff→0), Fig2 Luminosity spike at 5-6kpc (wave energy dissipation), Fig3 Bar-spiral ratio clustering at 1:2, 1:3 locks (standing wave J_l(k r0)=0), Fig4 Flat bar + spike r_cR/r_B~1.2 (NGC1300), Fig5 R_CR/R_bar jump 1.12→1.47 at Vcrit, Fig6 Pitch angle std 6.7°→11.8° (damping increase). Relation to Previous Work & Deprecation Notice This work fully supersedes and obsoletes 10.5281/zenodo.22709672 (Spatium Lacunosum v1.6). The previous model was based on: Space = d²S/dt², Pendulum Universe, Onion Shell Model Fluid Cut mechanism V_flow + V_bar + V_inertia = 0 Tidal locking resonance and ghost matter hypothesis These axioms are fully deprecated and abandoned in the present work and replaced by: Equiangular Spiral-Waveguide Formalism R = r₀·e^(±bθ)·e^(±iφ)·e^(±jψ) = r₀·G·R_ot·T_w Torque cut mechanism τ_eff(r)=τ0·T_w(r)·cos ψ(r), cos ψ≤0 → τ_eff→0 → r_cut Geometric extension of Lorentz factor with critical angle θ_c = arcsin(2/3)=41.81° File: 0final_Galaxy-Waveguide-Complete-English.pdf (14 pages, 6 embedded figures) Keywords: barred spiral galaxy, waveguide, phase flip, torque cut, Hoag's Object, PHANGS, S4G, R_CR/R_bar, equiangular spiral