The Temporal Classification of Stellar Objects: A Fractal Density Approach to Cosmology

We introduce a symmetry–aware framework for classifying stellar objects from their temporal signatures. The method composes two scaleinvariant detectors: (i) a fractal prior on the analytic-signal envelope, targeting a near-universal temporal dimension Dt 0:81 for intermittent yet persistent variability, and (ii) a multi-scale Laplacian-of-Gaussian (LoG) operator that highlights sharp transitions and edges in time. Their fusion, fusion = 1 􀀀 (1 􀀀 env)(1 􀀀 LoG), yields a robust activation mask from which we extract invariants (Dt; ; 2) via multitaper spectra and structure functions, with 2 􀀀1 serving as a bridge consistency check (Press et al., 2007; VanderPlas, 2018). We formalize a three-channel interpretation of variability (thermal, gravitational, magnetic) and provide simple decision rules for class labels that are resilient to gaps, uneven cadence, and instrument systematics. On synthetic benchmarks emulating main-sequence stars, pulsators, eclipsing binaries, flare stars, and AGNlike sources, the pipeline recovers class-specific fingerprints with high separation in the (Dt; ; 2) space and low confusion under realistic noise. The design is CPU-friendly, avoids temporal smoothing (which erodes discriminative power), and is directly applicable to TESS/Kepler/ZTF light curves. We conclude with cosmological implications of a recurrent Dt prior and a roadmap for falsifiable tests.