The framework proposes four incidents, Signal, Context, Coincidence, and Potentials, as the foundational functions of existence, the conditions anything must satisfy to occur at any scale in any domain. Four axioms (Existence, Space, Time, Energy) are proposed, from which the sequential ordering, the dual-axis organization (boundary/interior crossed with input/output, 2² = 4), and the irreversibility of completed forms are derived. The four foundations of mathematics (logic, set theory, type theory, category theory) formalize the four incidents in this sequence, composing through established correspondences into an endomorphism, a structure-preserving map from the system to itself. The framework derives the direction of time and the structural distinction between past, present, and future from the irreversibility of completed forms. Frameworks developed independently across different centuries, disciplines, and methodologies each arrived at the same four-part structure. None derived it from the others. The framework proposes they converged because they reached the same substrate. Apparent three-part systems compress two structurally distinct operations into one position; the missing fourth is recoverable in each case. Three testable predictions are advanced, each falsifiable by a single counterexample. The complete tenant map of twenty-six converging frameworks is presented in the companion supplement (Stewart, 2026, Supplement). The analysis of eight apparent three-part systems is presented in a companion paper (Stewart, 2026, Apparent Threes). **Keywords:** formal ontology, foundational device, occurrence, four-incident form, cross-domain convergence, endomorphism, dual-axis organization, 2² structure, Curry-Howard-Lambek correspondence, category theory, quiver path algebra, Hamiltonian cycle, gauge algebra, bilinear invariant, recursion, irreversibility
Arthur Stewart (Thu,) studied this question.