Abstract

We present a mathematically rigorous extension to quantum mechanics that accounts for consciousness while resolving longstanding paradoxes in physics. Through formal set-theoretic, group-theoretic, and category-theoretic arguments, we first demonstrate the logical impossibility of emergentism—the view that consciousness arises from complex physical processes. We then introduce a minimal dual-phase space framework in which physical states exist in a Hilbert space HΨ and phenomenal states in an orthogonal Hilbert space HΦ , connected by the awareness operator A and volition operator V. These spaces maintain a precise π/2 phase relationship, with the resultant complex energy eigenvalues manifesting gravitationally as dark matter and dark energy. Our framework elegantly resolves the quantum measurement problem through the Born Rule Locus Correspondence (BRLC), which establishes that phenomenal probabilities exactly match physical probabilities when properly referenced to the observer's spacetime locus. We derive several tensor product norm identities that explain both the causal efficacy of consciousness and its imperviousness to physical detection. Finally, we demonstrate how our framework necessitates the persistence of consciousness beyond biological death through phase decoherence and recoherence processes that follow directly from the mathematical structure. Throughout, we identify specific empirical predictions that distinguish our framework from competing theories. The A|Ω⟩ formalism thus unifies quantum mechanics, consciousness, and cosmology within a single mathematical structure that preserves logical coherence while remaining empirically testable.