Scale-Time Theory

Scale-Time Theory: The Geometry of Scale-Space presents a pre-physical framework in which physical-looking behavior is treated as the projected readout of deeper phase-closure dynamics. The framework begins not with spacetime, matter, fields, or forces, but with a two-dimensional scale-plane carrying four symmetric oriented coordinates, a central phasor, and a radial scale coordinate. Stable systems are modeled as scale-modes: antipodally closed circular phase structures whose diameters span integer numbers of phasor cycles. The theory distinguishes three structural layers: phase closure, coordinate-level read/write dynamics, and system-relative projection. Phase closure may occur anywhere on a scale-mode, while read/write events occur only when closure locks to one of the readout-coordinate rays of a system-local quadrature frame. Every stable system establishes its own local phase origin; an observer is treated as a nested system whose local reference functions as an aperture coordinate and whose passive readout window receives delayed projections of already-written outcomes. Within this architecture, the manuscript develops structural interpretations of spin-like aliasing, charge-like closure offsets, photon-like synchronization, rest-energy-like scale-position content, momentum-energy-like kinematic phase-gap content, gravity-like projection warping under incomplete containment, free-fall-like passive projection-warp descent, and spatial distance as projected inter-system phase distance. These constructions are presented as internal framework structures and candidate correspondences, not as completed derivations of physical spin, charge, photons, gravity, rest mass, or space. The work is intended as a formal and conceptual substrate model for investigating how quantum-like and relativistic-looking regimes may arise from a common pre-spacetime phase-processing geometry.