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9. Recurgent Field Equations and Global Dynamics

This section develops the global dynamics of the coherence field $C(p, t)$ across the semantic manifold $\mathcal{M}$. Beginning with the foundational field equations, RFT traces how meaning propagates through recursive structures, gives rise to attractors, undergoes phase transitions, and interacts with interpreting agents.

Table of Contents

  • 9.1-9.5 – Core Field Equations
    The foundational equations that describe coherence propagation, semantic geodesics, metric evolution, and the recursive flows that reshape semantic space.

  • 9.6 – Bidirectional Temporal Flow
    Formal treatment of temporal asymmetry in semantic systems, where causality radiates outward from meaning concentrations while information signals move inward, shaping the phenomenology of time.

  • 9.7-9.8 – Global Attractors and Bifurcation Geometry
    Analysis of attractor evolution, phase transitions, and the geometry of critical points where semantic structures reorganize, including tools for detecting transitions in noisy systems.

  • 9.9 – Metric Singularities and Recursive Collapse
    Exploration of singularities in semantic geometry: attractor collapse, bifurcation points, and semantic event horizons where meaning becomes ensnared in recursive loops.

  • 9.10-9.12 – Agents, Interpretation, and Semantic Particles
    Interpretation formalized as active operator action on the coherence field, the emergence of agent-like structures, and the particle-like excitations of meaning that traverse the semantic landscape.

  • 9.13 – Symbolic Compression and Recurgent Abstraction
    Approaches to compressing complex semantic structures while retaining the core dynamics—covering hierarchical manifolds, meta-recursion, and scale-dependent transformation of semantic laws.

  • 9.14 – Epistemic Pathologies and Semantic Healing
    Taxonomy of pathological semantic structures, their mathematical signatures, and strategies for detection and remediation through wisdom-guided intervention.

Sections 9.1-9.14 assemble a dynamical systems framework for tracing how meaning emerges, stabilizes, transforms, and recovers through recursive processes. The theory weaves together continuous field dynamics and discrete semantic structures, grounding both the fluidity of meaning and its crystallization into stable patterns of understanding.

Next: Core Field Equations