Reset Dynamics, Paper 15 Extra1: Structural Cost Barriers and a Constructive Microscopic Mechanism for Emergent Time

This paper provides a constructive microscopic mechanism for emergent time within the Reset Dynamics model by embedding macroscopic phenomenological primitives into the Dissipative Numeral System (DNS) cost-hierarchy framework. We demonstrate that: (1) the phenomenological consistency ratio R ≤ 1 corresponds to the radix cost boundary condition C_{M+1} ≥ Γ, where available budget fails to support the creation of the next structural layer; (2) macroscopic entropy is modeled as a coarse-grained projection of accumulated tension trapped at the structural zero 0_T; (3) the Reset step is formulated as a state-space re-embedding operator with a Landauer-inspired dissipation bound ΔS_jump = ε + ξ∑C_n (0 < ξ ≤ 1); and (4) emergent time is decoupled from background continuous time by founding the arrow of time entirely on the event-counting parameter τ_N = ∑ 1(E_i). This work closes the gap between microscopic DNS operator dynamics and macroscopic temporal emergence, providing a complete tri-level cascade: Microscopic Structure (DNS) → Mesoscopic Threshold-Induced Reconfiguration (Reset) → Macroscopic Emergent Arrow (Time). Version 2.1 incorporates terminology refinements, clarifies key mathematical definitions (tension integration intervals, reset rules, order parameters), and adjusts claims to their appropriate scope within the model.