The 0.13 Curvature Gate: Vector Coherence, Embodiment, and the Entry into Lived Space

Coherent systems may be fully described through vectors alone. Curvature does not need to be added mathematically to generate structure. Instead, curvature emerges as an experiential threshold when coherent vectors are embodied. This paper identifies a consistent transition point—here labeled the 0.13 curvature gate—at which vector coherence enters perceptual, biological, and temporal realization. The gate marks the shift from abstract coherence to lived space. It is not a force, mechanism, or distortion, but a hinge through which coherence becomes experience. The 0.13 gate appears across geometry, biology, perception, and time as a stable phase offset that allows space to be occupied without collapse. coherence, vector geometry, curvature gate, 0.13 offset, embodiment, phase transition, torsion, Fibonacci curvature, 2.5D geometry, lived space, perceptual depth, biological coherence, nervous system stability, fascia, carbon lattice, electron flow, holographic reality, phase alignment, time emergence, stillness, plasma geometry, rotational symmetry, quarter turn, vector field, experiential physics, bioelectricity, consciousness geometry, curvature threshold, stability hinge, dimensional perception, field coherence, phase lock, embodied awareness, mathematical vectors, spacetime emergence, inner center, non-vortex stability, coherent technology, geometric embodiment, curvature entry, reality interface