From Meaning Networks to the Evolution of Complex Systems: Curvature Flow, BridgeStructures, and Technological Generation in Generalized Two-Dimensional Field Theory

This paper is the second in a series on two-dimensional feld ontology. The frst paper established narrow two-dimensional feld theory and the particle physics spectrum; the third paper addresses the curvature fow equation and the Millennium Problems. This paper answers a third question: how do complex systems evolve, and how can we operate on that basis? The paper is organized into three parts. Part I establishes generalized two-dimensional feld theory—a universal theory of complex-system evolution. The theory is organized around four question chains: evolvability (which systems can evolve?), hierarchical architecture (in what structure does evolution occur?), evolutionary dynamics (how does evolution proceed?),and structural universality (why is the theory cross-domain?). Core results include: the uniqueness theorem for the basic chiral charge; the chirality–time-arrow equivalence theo-rem; the chiral fow conservation law and the non-triviality of the chiral source; the stratifed confguration space and the cross-curvature fow theorem; the irreducibility theorem for three types of inter-level causality; the structural hysteresis theorem for hierarchical emer-gence and the principle of complexity accumulation; the joint unreachability theorem; the observer-internalization principle; the memory-kernel universality theorem; the three-level structure of experience-functional form evolution; the existence and critical region of mor-phological phase transitions; the intrinsic derivation of the decoherence time; the T-feld self-referential materialization and the subjectivity theorem; and the structural isomorphism theorem. Information theory does not appear as an independent chapter; it is demoted to a metric interpretation of the D-feld inner product and to a parallel formulation of chiral fow conservation. Part II establishes bridge structures—a formal conversion layer from abstract EDT to observable data. Part III presents technological generation and the verifcation matrix. The paper rigorously distinguishes“construction” from“verifcation”: Part I is at the level of theorems and principles; Part II is at the level of construction methods; all technological commitments in Part III are labelled“construction, pending verifcation.” ′We rigorously distinguish the linear decomposition V = A1⊕E from the trilinear invari-3∼ant∧ V = A2; we rigorously distinguish the three notions of weight C2, dim(R), and w(R)and their domains of applicability; the group-theoretic factorρS3 = 2/3 of memory-kernel enhancement uses the ratio of representation dimensions, not the ratio of Casimir invariants.The memory kernel is ontologically attributed to the D-feld autocorrelation; the E and 1 T ffelds do not carry historical propagation. This attribution implies that memory-kernel corrections of gauge channels are channel-dependent.