Scale-Time Theory

Scale-Time Theory (STT) - Version 3.0 is a reconstruction framework in which spacetime, quantum behavior, and gravitation emerge from a discrete readout process acting on a pre-geometric substrate. The theory starts from a spectral carrier evolving on a punctured 2D scale plane ℝ²∖{0} under a strictly monotone ordering parameter λ. A rotating dipole Source at the puncture drives a conserved throughput via the constant area-flux law k := dA/dλ, producing outward Scale Flux and an intrinsic spectral ramp. When the ramp reaches a distribution (readout) limit, a discrete reconstruction mechanism (the Master Sampler) nucleates at σ₀, defining the post-ignition architecture: time as a tick cadence, space as a finite-resolution lattice, and observable fields as inverse-Fourier readout from discretized spectral bins with Nyquist cutoff u_N = π/ℓ₀. Because sampling is filterless, aliasing is structural; STT treats the resulting non-injective readout (and its Fourier uncertainty bound) as the origin of quantum indeterminacy. A central derived quantity is the oversampling ratio OSR(σ) (set by scale-dependent render load under fixed per-slice capacity), yielding a scale clock: low OSR corresponds to quantum behavior near the representational edge, while high OSR yields classical stability on scale-harmonic structures. In this picture, gravity and time dilation arise from render-cost–driven scale-upshift (scale-upshift → Scale-Flux slowdown → clock slowing), and dark-matter phenomenology is reinterpreted as scale-clock running in high-σ systems. The post-ignition architecture naturally supports an effective (3+1+σ) view, with a compact scale coordinate enabling U(1) gauge structure. The document is organized as: Part 1: conceptual foundation and interpretive structure Part 2: explicit formalism and derivations (Unicode math throughout), plus symbol reference