A conscious experience feels unified and simultaneous, yet most artificial systems process information sequentially. This paper proves that this difference matters by augmenting Stack Theory with algebraic laws that relate within-time-window constraint satisfaction to conjunction. A system can realize all the ingredients of experience across time without ever instantiating the experienced conjunction itself. Two postulates are distinguished: Chord, requiring objective co-instantiation of the grounded conjunction within the window, and Arpeggio, requiring only that ingredients occur within the window. A measure called concurrency-capacity formalizes what is needed for co-instantiation. Neurophysiological evidence suggests consciousness depends on phase synchrony and effective connectivity; loss of consciousness is associated with its breakdown. Under Chord, software consciousness on strictly sequential substrates is impossible for contents requiring two or more simultaneous contributors.
Consciousness arises because organisms that learn to classify causes of their own sensations adapt more efficiently. The hard problem—why there is something it is like to be conscious—is resolved by showing that phenomenal consciousness (P-consciousness) emerges when an organism must classify its own interventions, creating a persistent quality across those interventions. Access consciousness (A-consciousness) emerges at a higher order when an organism must infer another's prediction of its interventions. Together they form H-consciousness, a hierarchy of causal identities that simplify the environment into classifiers of cause and affect. The authors deny that a philosophical zombie could be as capable as a P-conscious being, because learning causality requires presupposing objects, not just learning associations.
Taking the naturally selected, embodied organism as a starting point, the authors provide a formalism describing how biological systems self-organise to hierarchically interpret unlabelled sensory information according to valence. Such interpretations imply behavioural policies differentiated only by the qualitative aspect of information processing. Natural selection favours systems that intervene to achieve homeostatic and reproductive goals, and quality arises to link cause to affect to motivate interventions. Access consciousness at the human level requires hierarchically modelling the self, the world/others, and the self as modelled by others, which requires phenomenal consciousness. Phenomenal without access consciousness is likely common, but the reverse is implausible. The proposal lays a foundation for a formal science of consciousness.