Dissipative Numeral System, Paper 0.5: Structural Zeros — From Label to Generative Skeleton

This paper introduces the concept of the DNS structural zero 0_T within the Dissipative Numeral System (DNS) framework. Unlike the classical algebraic zero as a context-free identity element, the DNS structural zero is defined as a special object in the DNS structural state space, characterized by zero occupancy and non-zero structural cost. The paper distinguishes between generation cost, which is explicitly represented as a vector in the structural space, and algebraic cost, which remains zero to preserve compatibility with classical algebra. It formulates the structural zero as a hierarchical object indexed by a generative skeleton tensor T, and proposes formal propositions on structural identity, non-trivial generation cost, and state transition constraints. This work serves as a bridge between DNS Papers 0, II, III, IV, and V, and establishes structural zero as a foundational concept for the DNS series.