ATPEW V11.65: Beyond the Stellar Pseudo-Vortex — Hierarchical Decomposition into Stellar, Galactic, and Group-Scale Energy Vortices in SPARC Galaxies

We present ATPEW V11.65, a major conceptual extension of the Primordial Energy Wave (ATPEW) framework for galactic dynamics. Unlike previous single-vortex formulations, this version introduces a hierarchical tripartite structure of energy-wave vortices acting across multiple astrophysical scales:
(1) a stellar pseudo-vortex arising from the statistical interference of billions of stellar micro-vortices,
(2) a coherent galactic vortex emerging at large radii, and
(3) a group/cluster-scale vortex representing intergalactic environmental coupling.

The stellar pseudo-vortex is modeled as an interference field whose amplitude may be constructive or destructive, naturally explaining the observed suppression of inner rotation velocities in compact bulges without invoking ad hoc braking mechanisms. Its strength depends on local surface density, environmental flux, and an interference phase governed by a smooth transition function. The galactic vortex emerges progressively with radius, while the group-scale vortex introduces a large-scale coupling term that becomes relevant in extended disks and dense environments.

The model is applied to the full SPARC sample of 175 galaxies using automated parameter optimization. ATPEW V11.65 achieves a global RMS residual of 2070 km/s, improving upon ATPEW V9 (2690 km/s) and MOND (3637 km/s). The improvement is particularly strong for low-surface-brightness galaxies and compact massive systems, where destructive pseudo-vortex interference resolves long-standing discrepancies between baryonic predictions and observed rotation curves.

The hierarchical vortex structure provides a physically motivated alternative to dark matter halos and ad hoc interpolation functions, suggesting that galactic rotation curves may arise from scale-coupled phase structures of an underlying energy field. The model yields several testable predictions, including correlations between pseudo-vortex parameters and observed stellar kinematic support (v_rot/σ), and between group-vortex strength and galaxy environment.

ATPEW V11.65 thus represents a transition from a phenomenological single-scale correction to a multi-scale emergent dynamical framework for galactic rotation.