FRA: Dark Matter as δ-Interference, Dark Energy as Fractal Growth

Known Discrepancies and Methodological Limitations This release provides a working operational prototype, but it also exposes several systematic limitations in the NGC 2403 test case. 1. Outer Rotation Curve Deviation The FRA-derived dark-matter component VDM (FRA 1D) captures part of the inner rise, especially in the 2–6 kpc region, but declines too steeply at larger radii compared with the observationally inferred VDM (obs). This indicates that the current 1D proxy, default channel weights, and smoothing scale do not yet fully reproduce the extended outer-halo contribution. 2. Geometric Approximation The present mass recovery uses a spherical approximation: M (<r) = ∫ 4πr² ρ (r) dr. For flattened disk galaxies such as NGC 2403, this can introduce systematic bias in the recovered density and velocity profiles, especially at large radii. A future version should replace this step with an axisymmetric disk potential or a numerical Poisson solver adapted to disk geometry. 3. Kinematic Proxy for δ In this v2. 0. 0 release, the FRA contrast field δ is derived from radial gradients of SPARC velocity components, such as Vgas, Vdisk, and Vbul. These quantities already encode part of the gravitational structure that the model later attempts to reconstruct. Therefore, this version should be treated as an operational reconstruction prototype, not yet as a fully independent prediction. A fully predictive v3. 0+ version should derive δ from structural maps independent of rotation-curve kinematics, such as gas surface density Σgas, stellar photometry, SFR maps, baryonic-potential gradients, and HI shear fields. 4. Calibration Scope The coupling coefficient κ is currently calibrated at a single reference radius: Rₜarget = 8. 0 kpc. This is acceptable for a controlled single-galaxy prototype, but not sufficient for a universal claim. Statistical robustness requires testing κ across a larger SPARC sample and checking whether it remains stable globally, or at least within well-defined galaxy classes. 5. Current Status This release should be read as a phenomenological and computational prototype. It demonstrates the operational chain: δ → σ_δ → ρDM → M (r) → VFRA (r), but it does not yet claim to replace ΛCDM or standard halo models. Next steps include: - replacing kinematic δ-proxies with density-based structural δ-fields; - implementing disk-aware or axisymmetric gravitational recovery; - testing the method across the full SPARC sample; - comparing RMSE, χ², AIC, and BIC against NFW, MOND, and other standard models; - evaluating whether κ is stable globally or only within specific morphological classes. This limitation record is included intentionally to make the prototype falsifiable, reproducible, and methodologically transparent.