The Present as a Dynamical Engine: Observer-Driven Expansion and Stability Constraints in the ΔH-Δt Framework From 0 to ∞ via State-Space Expansion and Responsibility Constraints

TITLE The Present as a Dynamical Engine: Observer-Driven Expansion and Stability Constraints in the ΔH-Δt Framework From 0 to ∞ via State-Space Expansion and Responsibility Constraints ABSTRACT We propose a dynamical framework in which the universe is modeled as a feedback loop between an Observer-System and its Environment, initiated from a null state with no accessible states. The act of measurement defines the first inaccessible state. The conversion of inaccessible to accessible states initiates dynamics and expands the state-space as N=2^2. We formalize this as the Escalation Law: for every state conversion, the Environment generates a new, more complex boundary condition. This mechanism is mapped onto a previously established ΔH- Δt framework, where gravitational wave amplitude scales as AGW∝d and AGW∝dtd(Δtmod). Total entropy dynamics are conserved via ΔH(past)+ΔH(present)+ΔH(future)=const. We derive a Stability Constraint Tensor R=B/W with deployment condition R≥1. We further show that cessation of the exploration rate dtd(Δtmod) leads to a collapse condition Δt→0. Case studies in nuclear physics, artificial intelligence, and climate engineering demonstrate the necessity of this regulation for system stability. The results suggest that continuous information processing in the present state is required to maintain expansion and avoid collapse. This framework provides a physical mechanism connecting measurement, state-space growth, and stability across scales. Keywords: ΔH- Δt framework, dynamical systems, state-space expansion, stability constraints, gravitational waves, observer-system