The Emergence of the Living Attractor: Non-Equilibrium Dissipative Selection, Casimir Variational Localization, and the Inevitability of Autocatalytic Chemical Networks

The origin of life (abiogenesis) presents a foundational paradox in modern physical science: how an undifferentiated prebiotic chemical mixture spontaneously transitions into a self-replicating, metabolically active proto-organism without violating the second law of thermodynamics. Refuting traditional statistical impossibility arguments, this work establishes an open-system non-equilibrium dissipative framework proving that the spontaneous emergence of life is a dynamical inevitability with Lebesgue measure one. We formulate a universal open-system reaction-diffusion manifold coupling an external substrate monomer influx (M_0), non-catalytic linear waste polymers (X), and closed cyclic autocatalytic networks (A, reflexively autocatalytic sets). Grounded in Casimir variational decomposition, Willems dissipative inequalities, and Perron-Frobenius spectral theory, we prove and numerically verify three foundational theorems: Variational Spectral Selection Theorem: Open acyclic polymers possess nilpotent interaction spectra and experience exponential decay under finite substrate flux, whereas closed autocatalytic cycles maximize the principal Perron-Frobenius eigenvalue lambda_PF(W), selectively concentrating high-energy flux and exponentially outcompeting linear oligomers. Supercritical Dissipative Ignition Theorem: Exceeding a critical environmental substrate influx threshold (J_crit) collapses the local Koopman restoring gap (Omega_1,chem -> 0) and triggers a supercritical pitchfork bifurcation, igniting an autonomous, high-flux living metabolic attractor (A_alive). Prebiotic Anti-Anthropic Attractor Theorem: Under finite physical boundary confinement (hydrothermal micro-pores or lipid vesicles serving as chemical analogs of T(T-bar) Dirichlet cutoffs) and non-vanishing thermal noise, the phase-space volume of permanently sterile, non-living trajectories vanishes identically (mu(Non-Living) = 0), making the transition into the living attractor occur with probability unity. Numerical Verification & Prebiotic Evolution: High-precision Runge-Kutta (RK45) simulations coupled with online Koopman spectral analysis confirm that living attractors emerge inevitably under micro-pore confinement (A_total -> 0.98 vs. dilution extinction in unbounded bulk), anticipated by Koopman spectral gap softening as J_in approaches J_crit ≈ 0.38. Furthermore, competing autocatalytic networks autonomously undergo prebiotic Darwinian selection governed by the Maximum Entropy Production Principle. Open Science & Reproducibility: This framework seamlessly bridges cosmological vacuum self-regulation (Papers I-VI) with macroscopic cellular and clinical pathology (Papers VII-X), identifying the living state as a universal self-organizing dissipative phase. The complete open-source Python simulation codes, differential equation solvers, parameter sets, and numerical trajectory datasets are publicly accessible under the MIT License at: https://github.com/sukuyoshi/abiogenesis_attractor (This treatise completes the universal dissipative attractor series spanning Papers I-X; DOI: 10.5281/zenodo.24112940 through 10.5281/zenodo.24156449).