The Measure of the Divine

The question of quantifying the probability of a Supreme Intelligence () has historically suffered from methodological deficiencies in classical epistemological probability. Standard subjective Bayesian models collapse into subjective arbitrariness, where priors are assigned arbitrarily based on epistemic bias, leading to uninformative or singular probability distributions. This paper proposes a mathematically rigorous framework, the Restructured Epistemic Probability Function (REPF), to formalize the likelihood of divine existence. By synthesizing Algorithmic Information Theory (AIT), Modal Logic S5 Model Theory, Measure-Theoretic Probability Space Extensions, and Transfinite Cantor-Gödel Operator Dynamics, we move beyond classical subjective probability. We construct an extended probability space over a non-Archimedean hyperreal field , allowing non-zero infinitesimal assignments to necessary truths, thus preventing prior saturation and zero-locking singularities. We utilize Solomonoff-Kolmogorov Complexity to establish that a universe capable of supporting conscious observers exhibits algorithmic fine-tuning whose information density asymptotically approaches the upper limit of natural complexity bounds without an intentional generating function. Modal collapse is circumvented using higher-order hyper-dimensional continuous spaces where the probability density operator evaluates to 1 in the limit of maximal information-entropy minimization. We offer formal proofs, mathematical formulations, MindMaps showing the flow structures, open questions in formal theology-physics, and future directions for research.