ALADIN Plasma Stability Law v0.5 — Invariant Threshold for Causal Self-Stabilization in Current-Driven Plasmas

This release presents v0.5 of the ALADIN Plasma Stability Law — a first-principles force-balance criterion for self-stabilization in current-driven plasma columns (Z-pinches) against sausage m=0 and kink m=1 instabilities. The law is anchored to a single experimentally accessible parameter — the axial current density J_0 = 1.000 \times 10^{18},A/m^2 — and an invariant threshold \Pi = that arises from relativistic causality constraints on Alfvénic signal propagation v_A^{rm rel} le c / sqrt{2}. The threshold \Pi = is derived exactly from the magnetic-rest energy balance point P_{rm mag} = ρ_{rm eff} c², where the classical Alfvén speed formally reaches v_A = \sqrt{2}\, c, signaling the breakdown of non-relativistic MHD. The physical (causal) Alfvén speed is bounded by v_A^{\rm rel} \le c / \sqrt{2}. Stabilization emerges naturally when QMHD back-reaction (Schwinger pair production and quantum degeneracy pressure), relativistic flow corrections, Kerr-like GR effects (phenomenological), turbulence damping, reconnection feedback, and multi-mode tracking increase \rho_{\rm eff}(t) to enforce \Pi(t) \ge — without any imposed suppression terms. The included script demonstrates 1D time-dependent collapse with pure force-balance dynamics. A separate falsification grid verifies runaway collapse for initial \Pi < in the absence of stabilizing mechanisms. Previous versions v0.2: 10.5281/zenodo.18306470 v0.3: 10.5281/zenodo.18313105 v0.4: 10.5281/zenodo.18319371 Repository https://github.com/aladinibz/AladinEquationVinfinity License MIT