Whether conscious experience is substrate-independent—capable of arising in any physical system that implements the appropriate computational or dynamical structure—remains a central challenge in philosophy of mind and consciousness science. This paper proposes the Container Hypothesis, a formal framework grounded in the mathematics of open quantum systems to establish substrate independence on rigorous footing. We define a container as a four-tuple (H,H,{L_k} {γ_k})comprising a Hilbert space, system Hamiltonian, a set of Lindblad (jump) operators, and corresponding coupling rates. Within this framework, we introduce two quantitative measures: Quantum Substrate Specification (QSS) efficiency, which quantifies how effectively environment-assisted processes—analogous to noise-assisted quantum transport—maintain coherent information flow; and Quantum Entanglement-correlation Fidelity (QEF) strength, which captures multi-partite quantum correlations available for information integration. We define container equivalence using the diamond norm on completely positive trace-preserving (CPTP) maps, providing a rigorous criterion for when two physically distinct substrates may be considered dynamically—and potentially phenomenologically—equivalent. We derive several relationships between QSS and QEF and established measures in quantum information theory and Integrated Information Theory (IIT), and propose two experimentally testable predictions involving two-dimensional electronic spectroscopy of candidate biological structures and correlational neuroimaging studies. We explicitly acknowledge that this framework does not address the hard problem of consciousness, operates under significant empirical uncertainty regarding biological quantum coherence timescales, and should be regarded as an exploratory formal proposal rather than an established theory.