The First Cut: How Boundary Logic Derives Physics

AbstractWe begin with a single primitive act: cutting from a background to make a distinction. This“first cut” establishes a bounded entity against an indeterminate ground (Apeiron). We show thatpersistence is not a state but a cybernetic process: identity is maintained through the inte-gral of corrective work against decay over time. From the symbolic form A(t) = ¬t |¬t0 A|, weimmediately derive the integral form A(t) = A0 + (Φ − N )dτ —the historical ledger of allmaintenance acts. This integral is the foundation: its optimization yields the differential balancelaw dA/dt = Φ − N , recovers classical logic as its zero-maintenance limit, and necessitates theSecond Law of Thermodynamics. Calculus emerges as the native mathematics of this mainte-nance process, and physics as its domain-specific expression. The framework unifies geometry,dynamics, and cybernetics into a single first philosophy. Finally, we apply this calculus to classi-cal metaphysics, demonstrating that the maintenance integral resolves long-standing paradoxesof material identity—such as the Ship of Theseus—by defining existence not as static substance,but as a continuous history of entropic resistance.