Functional Consciousness: Pillar 45 - A Mathematical Framework for Recursive Registration and Consciousness

From Distinction to the Observer: A Mathematical Framework for Recursive Registration and Consciousness

This preprint proposes a distinction-first account of observation and consciousness. It begins from Axiom D: physically different states require distinguishability, whether or not any observer registers the difference. From that starting point, the paper builds a staged architecture in which a persistent system B comes to register another system A, retains the history of those encounters as memory, internally represents its own participation in the registration, and uses those representations in its ongoing dynamics. Each stage is formalized in a short set of equations, with the conditions under which it counts as registration, memory, or self-representation stated explicitly.

The consciousness hypothesis is kept separate from the architecture. It holds that experience is the intrinsic, system-specific aspect of a sustained process in which distinctions are registered and the system’s own participation is internally represented and causally incorporated. The paper identifies this as a bridge hypothesis, not a derivation, and states plainly that it does not yet specify a calculable mapping, an experiential unit, or a consciousness threshold. It closes with a research program built on four interventions: altering registration, disrupting retained history, altering self-representation, and interrupting causal incorporation.