The Geometry of Conscious States: A Five-Dimensional Framework

Most measures of conscious state reduce neural dynamics to a single number, and each tends to work on one kind of state transition and poorly on another. This paper characterizes the geometry of EEG state transitions instead: conscious state as a position in a multichannel space, and a transition as a trajectory carrying both a magnitude and a direction, where the direction reports how a brain left waking, not only how far. On three cohorts spanning two transitions (natural sleep from waking to deep sleep, and two propofol sedation paradigms), the sleep and propofol group trajectories are directionally distinct, close to orthogonal, and separable on per-subject dispersion. Sleep exits waking through consistent combinations of the channels, while propofol exits through heterogeneous combinations scattered around a stable group direction. The load-bearing results are geometric and are computed on the channel vector; the composite scalar is reported for completeness but is explicitly lossy and not load-bearing, and the geometric findings are computed without reference to it. The direction result also does not rest on the framework's proxy-sensitive interaction channel: removing that channel outright leaves the primary inter-paradigm angle essentially unchanged, moving from 83.7 degrees to 82.8 degrees. Because complete removal is the extreme of any possible correction, a direction that survives it survives any partial recomputation as well, so the geometry is robust to the proxy in the worst case, not merely the expected one. Two independent witnesses agree that the framework's fourth factor, spectral complexity, and its organization channel are not redundant in these data: the two axes are close to orthogonal as transition directions, and their within-state correlation is weak and inconsistent in sign across cohorts (about minus 0.2, plus 0.2, and minus 0.3). A pre-specified search over seven literature-supported candidate dimensions produced none that met the stated criterion. Recurrent feedback is defined as returning mutual information, with the normalized spectral radius as its linear sub-critical estimator, and every reported value lies inside that estimator's licensed range.