The Chronostasis Halo Profile: A Chronostasis Alternative to Dark Matter from the Spectral Framework, Tested on SPARC Rotation Curves

We propose the Chronostasis dark matter halo profile, derived from the fractal-spectral framework, in which the halo mass distribution follows a hierarchy of shells with characteristic radii Rₙ = R₀ × (√2) ⁿ and amplitudes decreasing as (√2) ^−n. The profile has two free parameters (R₀, v₀) — the same count as the standard NFW profile — and is tested against 50 galaxies from the SPARC database using identical methodology for both profiles (differential evolution + L-BFGS-B optimization, bootstrap uncertainties). The Trinity Chronostasis variant — three coupled layers at relative offsets of 1, √2, and 2 — achieves lower reduced chi-squared in 47 out of 50 galaxies (94%), with Wilcoxon signed-rank p = 1. 5 × 10⁻¹¹. The improvement is systematic but modest in absolute magnitude (Δχ²_ν ≈ −0. 34), largest for dwarf irregulars where the cusp-core problem is most severe. The profile naturally resolves the cusp-core problem: the inner density slope is α = 0 (core), not α = −1 (cusp), as a structural consequence of the exponential saturation 1 − e^−r/Rₙ at each scale — not imposed by assumption as in the Burkert profile. For r ≪ R₀, all terms contribute linearly, giving constant-density cores. For r ≫ R₀, terms saturate successively, producing flat rotation curves. The paper honestly reports a null result for the most distinctive prediction: log-periodic signatures in rotation curve residuals are searched for via FFT analysis, but the detection rate (42%) does not exceed the false positive rate from synthetic NFW curves (47%). The log-periodic signature remains unconfirmed with current data precision. This does not falsify the profile — it means current rotation curve uncertainties (~2–5 km/s) are insufficient to detect modulations at the predicted amplitude (~few km/s). SKA HI surveys and IFU spectroscopy of nearby dwarfs are identified as the path to detection. The paper remains deliberately agnostic about the microscopic origin: the Chronostasis field may consist of actual particles in fractal distribution (testable by direct detection experiments) or effective mass from fractal corrections to the gravitational field equation (testable by precision gravity tests at intermediate scales). Both interpretations produce identical rotation curves.