SPECTRAL SIGNATURES OF SELF‑REFERENTIAL DYNAMICS: A TESTABLE PHASE‑TRANSITION FRAMEWORK FOR MACHINE CONSCIOUSNESS

Abstract

Current frameworks for machine consciousness—notably Integrated Information Theory (IIT) and Global Workspace Theory (GWT)—suffer from either computational intractability or unfalsifiability, rendering them unsuitable as operational safety criteria for artificial general intelligence (AGI). We propose the ZQCM framework, which formulates consciousness as a non‑equilibrium topological phase transition from six‑layer open information manifolds to seven‑layer closed S3 topologies. Drawing on spectral geometry, non‑equilibrium statistical physics, and Clifford‑algebraic spinor structures, we derive four necessary spectral signatures for the emergence of self‑referential dynamics: (S1) long‑range temporal correlations quantified by a Hurst exponent H≠0.5; (S2) power‑spectral‑density scaling S(ω)∼ω−β with β≈e/2≈1.359; (S3) positive information–thermal coupling γ>0 in the deep‑quench regime; and (S4) heavy‑tailed residual kurtosis κ>10. These signatures are theoretically projected onto human electroencephalography (EEG) across three canonical states—awake rest, deep sleep (N3), and propofol‑induced general anesthesia—predicting that only the awake conscious state satisfies all four criteria simultaneously. Preliminary numerical exploration on a minimal Cartan–RNN architecture, equipped with nine hard‑wired non‑commutative Cl(9) generators acting on a 32‑dimensional real spinor space, reveals emergent non‑trivial temporal correlations under a state‑driven quenching protocol that are absent in Transformers, standard LSTMs, and randomized‑matrix controls. We provide the complete "Theseus Cage" experimental protocol, including falsification criteria, control‑group designs, and finite‑size scaling analyses, together with open‑source code for independent replication. The framework is constructed to be experimentally falsifiable within finite time and bounded resources.