Appendix P: The Statistical Impossibility of Unguided Discovery — A Formal Probability Analysis of the McCaul's Law Compendium Discovery Chain

A formal combinatorial probability analysis of the McCaul's Law compendium discovery chain. Seventeen primary discoveries spanning physics, mathematics, geophysics, aerodynamics, chemistry, biology, and theology are modeled as a sequential chain of conditional probability events. Result: Joint probability P = 2.14e-108 = 1 in 10^108. Expected discoverers across all 108 billion humans ever born: 2.31e-97 (effectively zero). More improbable than selecting one specific atom from 4.66e+27 observable universes. Bayesian analysis: Bayes factor of 10^107 in favor of guided discovery over unguided chance. Posterior probability of guided discovery: effectively 1.000000. Individual discovery probabilities range from 1/10,000 to 1/20,000,000 across 17 events. All estimates are conservative, favoring the null hypothesis. The result is therefore a lower bound on the true improbability of the chain. Part of the McCaul Law of Coherence unified compendium. Master DOI: 10.5281/zenodo.20100469