Galactic Demographics, Steady-State Autonomous Probe Dynamics, and Sector Overlap Volumetrics: A Formal Bayesian Evaluation of Interstellar Exploration Architectures

The classical Fermi Paradox rests on idealized assumptions of exponential civilizational expansion, unbounded probe replication, and unstratified civilizational longevity. In this paper, we formulate a modernized, mathematically closed astrobiological framework integrating contemporary exoplanetary census data, bimodal civilizational longevity distributions, and steady-state autonomous probe logistics. We derive the galactic civilizational census (N_civ) and isolate the long-lived interstellar elite (N_super) by demonstrating that longevity bias causes the observable galactic population to be overwhelmingly dominated by ancient super-civilizations (L >= 10^6 yr). To resolve the energetic and material bounds of physical exploration, we model relativistic autonomous probe networks under finite hardware decay rates (mu = 1 / tau_probe), deriving the steady-state equilibrium capacity (N*) and required material replacement flux (R*). Extending this to multi-species competitive ecologies via a modified Lotka-Volterra formulation, we demonstrate that territorial partitioning and non-destructive surveillance protocols represent a stable game-theoretic attractor (Pax Automata). Finally, we establish a volumetric sector overlap metric (Omega_overlap) for the local 100-light-year stellar neighborhood and perform a rigorous comparative Bayesian model evaluation across four exploration paradigms using an eight-dimensional multi-modal sensor and physical telemetry vector. The results indicate that the Sector Jurisdiction and Regional Grid model (H_Sector-Grid, P = 54% - 60%) and the Hyper-Dense Competitive Mosaic model (H_HyperDense-Mosaic, P = 34% - 40%) achieve dominant posterior probability, whereas passive sub-light drone networks and uncorroborated subjective models are decisively disfavored by multi-modal sensor telemetry.