Black Pearl

Black Pearl develops a computational and mathematical framework for analyzing dependency, causation, necessity, essence, sufficient reason, mereology, grounding, and ultimate explanation within an Avicennian architecture. The book formalizes material, formal, efficient, and final dependency as typed relations, integrates them with the Pensive cognitive architecture, and studies structural questions involving foundation, explanatory coverage, modal invariance, causal arity, regress, minimal cause, and vertical grounding. Its central scientific contribution is to identify which explanatory properties can be finitely verified, which require additional bridge principles, and which global decision problems become computationally undecidable on sufficiently expressive effective classes. The result is a formal theory of how finite intelligence can represent, test, and operate over complex explanatory structures without collapsing uncertainty, non-resolution, and metaphysical status into one another.