The Mathematics of Becoming: Reality, Relation, Differentiation, Boundary, and Vulnerability

Reality becomes mathematically accountable only when its objects, relations, boundaries, assumptions, and failure conditions are declared. The Mathematics of Becoming: Reality, Relation, Differentiation, Boundary, and Vulnerability begins with equation passports, simulation, reproducibility, and falsifiability, then moves through state spaces, observables, invariants, graphs, networks, morphisms, couplings, partitions, symmetry breaking, topology, interfaces, flux, perturbation, sensitivity, and failure.Aston Gustavous Farquharson presents these mathematical languages as disciplined tools rather than universal mechanisms. Similar formal structures may appear across physics, biology, ecology, persons, institutions, and civilizations, but cross-domain resemblance does not erase differences in scale, evidence, embodiment, history, or causation. Vulnerability is distinguished from weakness; exposure from damage; failure from blame; and every formal classification remains subordinate to equal human dignity.Six canonical figures make the architecture visible: Ma'at and Relational Balance; Pre-Geometric Relation; Geometrogenesis; Differentiation and Identity; Boundary and Interface; and Vulnerability and Failure. Permanent chapter, equation, figure, and figure-slot identifiers connect this independent volume to the wider fifteen-volume Mathematics of Becoming sequence. Reality remains the measure.