The Symfield Dimensional Dymaxion: A Coherence-Topology Model for Human Knowledge and Living Systems (V1.2)

Abstract This paper reinterprets Buckminster Fuller’s Dymaxion geometry as a resonant topology for mapping human knowledge, living systems, and AI coherence. Rather than a static cartographic projection, the Dimensional Dymaxion functions as a dynamic diagnostic engine, transforming Fuller’s folds into a multi-layer coherence map where knowledge domains drift, collapse, and realign across a resonance Z-axis. The model introduces a six-domain knowledge lattice (Perceptual, Procedural, Symbolic, Relational, Recursive, Field-Coherent) and dimensionalizes it with depth as coherence rather than hierarchy. It offers a diagnostic grammar for collapse and recovery cycles (C∮∠∴) and a contextual membrane, Operator 𝕏, encoding the state of the agent (human, machine, or system) that engages with the map. Applications span AI safety (hallucination mapping, context-modulated prompt scaffolding), trauma recovery (procedural fallbacks and field-based re-entry), and civilizational reset models (symbolic crust subduction and renewal). By leveraging asymmetry as a feature rather than a flaw, the Dimensional Dymaxion becomes a simulation tool for epistemic drift, symbolic overload, and system-wide coherence restoration. This work forms part of the Symfield research program on non-collapse computation and field-coherent architecture. It provides a practical foundation for researchers, system designers, and cultural theorists seeking to measure, simulate, and restore coherence across scales, from neural circuits to civilizations.