The Physicality of Complexity: A Structural-Differentiation Criterion for Generator/Selector Decoupling

Abstract

The Physicality of Scales (P6) derives QGD's object hierarchy from a behavioral criterion silent, by design, on internal organization; Behaviorally Free, Ontologically Determined (P50) needs exactly the distinction P6 does not draw, grounding epistemic free will in a Generator/Selector coupling available only "for a sufficiently complex" preonic aggregate — a condition stated, not derived. This paper derives it. Two finite, computable measures are defined directly on an aggregate's binding graph and P41's cardinality machinery: structural differentiation, Ξ(A), via a swap-and-compare test on the existing state-transition equation, and generative compression, κ(A,n), as the ratio of reachable to Generator-narrowed configuration counts. A four-condition threshold is then derived, rather than assumed, for when a Selector is physically opaque to its own Generator: topological absence of surplus binding channels, and a capacity bound extending P16's Landauer-grounded physical constructivism from construction cost to discrimination capacity, closing both brute-force and compact-rule routes to reconstruction. The result recovers P50's decision-locus/mere-aggregation distinction at the network scale as a special case of the same criterion, yields falsifiable structural predictions independent of numerical grounding, and is compared against Integrated Information Theory and algorithmic complexity, sharing IIT's differentiation/integration structure without its unbounded partition search or its lattice-architecture requirement, and sharing none of Kolmogorov complexity's unbounded-domain idealization already ruled unphysical by P16. One technical question is left explicitly open: whether partial, short-of-exact predictive self-access defeats the opacity criterion, a question this paper connects to Ismael's treatment of counterpredictive devices rather than resolving. A non-physical precursor to the Generator/Selector structure, from an unpublished 1998–99 manuscript by the present author under a prior surname, is noted and explicitly restricted to conceptual priority, carrying no argumentative weight in the physical derivation.