Dynamic Gate Numbers presents a unified theoretical framework in which gates are defined as irreversible constraints on future admissible trajectories, rather than as control operators, decision rules, or normative filters. The core contribution of this work is a precise formalization of irreversibility in terms of reachability: a transition is irreversible if, once excluded, no admissible future trajectory can recover it. Within this framework, gate numbers quantify the progressive loss of future admissibility, capturing structural limits on viability that cannot be reduced to scalar costs, utilities, or optimization objectives. The paper unifies previously separate notions of gates into a single structure with four mutually interpretable layers: Mathematical: idempotent projection operators and monoid homomorphisms with zero, Dynamical: viability-preserving filters exhibiting plateau behavior and asymmetric collapse, Cognitive: gate exhaustion as a discrete event necessarily generating questioning and exploratory dynamics, Geometric: admissible trajectory selection in state–history space. A central result shows that gate exhaustion is an event, not a continuous process, and that closure is unavoidable once admissible refinements are exhausted. This leads to a rigorous distinction between terminal closure, which destroys adaptive capacity, and boundary closure, which preserves viability by enabling external coupling. The notion of Structural Zero is introduced as a fixed point under admissible refinements. Crucially, zero is not treated as termination, silence, or emptiness, but as internal closure: a pause state in which internal exploration is complete while external coupling remains possible. Questions may persist after closure, but no longer generate new internal structure. The theory proves the impossibility of universal scalar representations of gate-constrained dynamics, demonstrating that no single optimization metric can faithfully encode future admissibility. Computational experiments illustrate plateau laws, tunneling versus hard gates, and delayed collapse phenomena, serving as validation of the theoretical predictions rather than as proofs. Dynamic Gate Numbers is positioned as an upper-layer extension of Yang Jihoon Dynamics, adding explicit treatment of gate history, irreversibility, and closure to an otherwise neutral dynamical framework. The theory is intentionally non-normative: distinctions such as terminal versus boundary closure are dynamical, not ethical. This work provides a foundational framework for analyzing viability, cognition, and systemic collapse across mathematical, biological, social, and artificial systems, while remaining strictly within a formal, non-teleological structure.