CB-BEN: The Critical Emergence at the Edge of Non-Coincidence

This theoretical manuscript introduces CB-BEN — the Critical Boundary of Being Emergence — as a hypothetical ontological singularity where irreducible difference gives rise to structure. Expanding on the previously proposed frameworks of ψ⁸ (the topology of retention) and Ξ⁰ (drifting asymmetry), this work explores the precise threshold at which their mutual non-coincidence generates Θ — the topology of structured persistence. Through symbolic modeling, a mathematical formulation, and philosophical exposition, the paper suggests that being may emerge not from substance or event, but from a critical and unresolved tension between pre-ontological fields. CB-BEN is presented not as a doctrine, but as a conceptual topology: a gesture toward the possibility that reality is born where difference resists collapse.