The Container Hypothesis: Substrate Independence Through Open Quantum System Dynamics

This paper proposes the Container Hypothesis, a formal framework grounded in open quantum system dynamics to establish substrate independence of consciousness on rigorous mathematical footing. A container is defined as a four-tuple (ℋ, H, Lₖ, γₖ) comprising a Hilbert space, system Hamiltonian, Lindblad operators, and coupling rates. The framework introduces two quantitative measures: Quantum Substrate Specification (QSS) efficiency, quantifying how environment-assisted processes maintain coherent information flow, and Quantum Entanglement-correlation Fidelity (QEF) strength, capturing multi-partite quantum correlations for information integration. Container equivalence is defined via the diamond norm on CPTP maps. The framework is demonstrated through an analytical two-site ENAQT model yielding a closed-form optimal dephasing rate and 14. 6% noise-assisted transport enhancement. Two experimentally testable predictions are proposed. This is an exploratory formal proposal; it does not address the hard problem of consciousness.