The PAO Invariant

Adaptive behavior is traditionally explained by introducing objective functions, rewards, incentives, fitness, or goals that bias the dynamics of a system. We propose instead that adaptive individuality rests on a single organizational invariant: informational closure,  the condition under which persistent informational state and transient stochastic computation form a closed causal loop, each conditioning and modifying the other indefinitely. We give this invariant a precise, substrate-independent definition and verify it exactly against two canonical realizations — bacterial chemotaxis and an engineered software organism built from a repository, an agent, and the hooks that couple them.
  
Following the transition from Newtonian gravity to general relativity, we show that once persistent informational state is treated as a geometry rather than an external force, both the coherence and the normativity of adaptive behavior follow without positing any further explanatory device. The central open problem — the construction of an information metric governing the accessibility of neighboring  futures — is posed here; a further companion paper later establishes that any sufficiently regular realization of the invariant admits  such a metric, leaving open not whether but which geometry any particular PAO realizes.
  
We argue that informational closure plays, for adaptive individuality, the role that symmetry and covariance play elsewhere in physics: a structural invariant that any adequate account of the phenomenon must respect, independent of substrate.
  
This paper is the foundation of a research program whose biological and engineering consequences are developed at length in two companion papers.