The Geometry of Discovery: Plausibility Gradients, Boundary Expansion, and the Architecture of Knowledge

Discovery unfolds as a geometric process rather than a linear accumulation of facts. Across science, biology, culture, and perception, knowledge advances by expanding coherent boundaries within an infinite field of possibility. This paper presents a unified framework for discovery based on plausibility gradients, boundary expansion, and phase-coherent evidence accumulation. The framework applies across disciplines and scales, describing how understanding stabilizes through geometry, resonance, and time. Knowledge emerges as structured coherence forming within uncertainty. discovery geometry, plausibility gradient, boundary expansion, coherence theory, phase locking, knowledge architecture, systems science, holographic inquiry, pattern stabilization, uncertainty structure, epistemic geometry, complex systems, resonance, scientific discovery, interdisciplinary framework, coherence center, open systems, phase coherence, evidence convergence, boundary dynamics, fractal knowledge, emergent structure, non-linear discovery, field theory of knowledge, perception geometry, adaptive inquiry, uncertainty navigation, epistemology, systems coherence, exploratory science, discovery framework, structural knowledge, pattern recognition, phase alignment, coherence fields, information geometry, discovery process, scientific method evolution, frontier science, boundary phenomena, knowledge expansion, invariant structure, universal inquiry