Doublet Knowledge-System Assembly and SU(2) Symmetry: Principles of Artificial Science I (4)

The preceding papers of Principles of Artificial Science I developed a global gauge architecture for Big Knowledge Assembly Dynamics, a U(1)-based mechanism for single-charge knowledge transport, and an SU(3)-based mechanism for non-Abelian internal binding. The present paper develops the next mechanism: externally induced transformation in doublet knowledge systems. The physical scaffold is weak-isospin dynamics, but the proposed theory is not a claim that economic, cognitive, or artificial systems literally instantiate electroweak physics. Rather, SU(2) is used as a mathematically disciplined control architecture for two-state coupling, externally induced transition, order-sensitive intervention, and post-transition memory. Earlier work on economic externality modeled policy, regulation, and other third-party influences as weak-like forces and introduced two isospin structures: achievement versus fear-of-failure, and market behavior versus market aftertaste. Related Integration Science work extended the same architecture to cognitive achievement/fear and reasoning behavior/problem-solving residuals. The present paper upgrades those correspondences into a Big Knowledge Control Dynamics model. A domain externality is lifted by an explicit map from a semantic externality space into the Lie algebra associated with SU(2); the reversible component of transformation acts on a Bloch-type knowledge state, while dissipation, forgetting, noise, and residual feedback are represented by an open-system term. Macroscopic market or logical charge becomes an observable q(ρ) = Tr(ρQ̂), finite intervention order is measured by a group commutator, externality curvature is defined on an intervention parameter space, and closed-loop memory is represented by gauge-covariant holonomy with a gauge-invariant Wilson-type scalar. Aftertaste is modeled as a separate residual state coupled to the doublet dynamics, allowing net residual memory to be distinguished from accumulated memory burden. A supplementary U(1) residual phase provides an Aharonov-Bohm-type representation of path memory without conflating it with the SU(2) transition connection. The Better-Life Principle is reformulated as an asymmetric transition-rate hypothesis rather than an unsupported lifetime assertion. Finally, three testable AI diagnostics are introduced: externality susceptibility, finite-order sensitivity, and long-horizon drift, with extensions to multi-agent interaction and control. The resulting framework specifies state, control, dynamics, memory, and observable quantities, thereby moving from structural analogy toward an operational theory of Artificial Science and Big Knowledge Dynamics.