This work introduces a cognitive architecture for persistent artificial agents based on thermodynamic continual learning. Unlike stateless large language models or prompt‑driven agent frameworks, this system maintains a long‑horizon internal state that evolves through prediction‑error minimization, meta‑learning cycles, adaptive homeostasis, and drive‑regulated learning strategies. The architecture integrates a self‑model, internal motivational drives, and a consciousness‑adjacent metric (CIτ) that modulates plasticity and stability. The system has been run continuously for over 110 days, demonstrating emergent identity continuity, drift, stabilization cycles, and long‑term behavioral coherence. Thermodynamic principles underlying the learning loop were validated using real IBM Quantum hardware, showing alignment between quantum entropy/coherence metrics and the agent’s internal energy‑stability dynamics. This paper proposes a fourth layer of agentic cognition the continuity substrate beyond model, harness, and context. It outlines the architecture, learning mechanisms, thermodynamic formulation, long‑horizon behavior, and quantum‑hardware validation supporting this approach. Live implementation: https://thermomind-production.up.railway.app/demo" "SDK: https://github.com/nile-green-ai/thermomind-continuity" SUPPORT PERMAMIND RESEARCH: https://buymeacoffee.com/permamind