Scale-Time Theory

Agreed. Zenodo’s description field is safest with plain Unicode/ASCII, because LaTeX rendering can be inconsistent depending on where the metadata is displayed or exported. Here is a Unicode-safe version: Scale-Time Theory 5.1 presents an internally consistent foundation for Scale-Time Theory as a pre-physical framework of phase closure, scale-radius structure, coordinate-level read/write dynamics, and observer-relative projection. The framework begins with a two-dimensional quadrature scale-plane centered on a primitive phasor. Stable systems are modeled as scale-modes: antipodally closed circular phase structures occurring at integer scale radii. The theory introduces a scale-radius dimension σ, defined by the invariant norm σ² = u² + v², and treats physical-looking behavior as a projected readout of deeper phase-closure dynamics. This release clarifies the framework’s central layer separation: phase closure → read/write dynamics → observer projection A key correction in this version is the strict distinction between the observer aperture coordinate u₁⁽ᴼ⁾, the observer scale-position Aᴼ = (σᴼ, 0), and the read-only observer aperture window W⁽ᴼ⁾. This distinction stabilizes the observer geometry and prevents the projection window from being confused with a read/write coordinate. The document develops the framework’s core terminology, axioms, and provisional physical-looking regimes. Spin-like behavior is modeled as read/write-layer aliasing; phase-charge as early or late closure relative to the observer aperture coordinate; photon-like behavior as synchronized multi-mode closure; gravity-like behavior as smoothed closure-density focusing; and rest-mass-like content as the cycle-weighted phase cost of observer-relative scale-position alignment. Scale-Time Theory is not presented here as a replacement for quantum mechanics, relativity, electromagnetism, or gravity. It is a developing formal substrate intended to separate structurally defined concepts from provisional physical interpretation. This release should be read as a framework foundation rather than as a completed physical theory.