Description This work develops a structured framework for the analysis of spiral-arm pitch angles (ψ) within the Phase Interference Universe Model (PIUM). The study does not present new observational measurements; instead, it establishes a clear and reproducible methodology for linking phase-based theoretical predictions to galaxy-scale morphological observables. The framework is explicitly organized into three layers. First, an analytic phase-geometric description shows that logarithmic spiral structure arises naturally from a minimal phase ansatz, yielding the relation tan (ψ) = m/k. Second, a minimal phenomenological dynamical model is introduced to explore the emergence and persistence of coherent spiral patterns under a simple phase-coherence constraint. These numerical results are presented as illustrative demonstrations rather than empirical claims. Third, a morphology–dynamics linkage protocol is defined, providing a transparent and auditable pathway for future comparison between spiral-arm pitch angles and kinematic properties of disk galaxies. The kinematic baseline is anchored to a re-analysed subset of the SPARC galaxy sample, using explicitly defined selection criteria and a deterministic outer-slope measurement procedure. While SPARC provides high-quality rotation curves and derived quantities (e. g. , Vflat and outer logarithmic slope), it does not contain pitch-angle measurements. Accordingly, this work specifies a two-stage strategy for future empirical analysis: (i) cross-matching external pitch-angle catalogues to the SPARC sample using standardized name normalization, and (ii) a direct measurement pipeline on imaging data based on fixed preprocessing steps, including deprojection, polar transformation, ridge identification, and logarithmic fitting. Preliminary attempts to utilize publicly available morphology proxies (e. g. , Galaxy Zoo classifications) did not yield a sufficiently clean or complete correspondence with the SPARC sample. This limitation motivates the need for a controlled and reproducible measurement pipeline, as defined here. The primary contribution of this work is therefore methodological. It provides a clearly defined, falsifiable, and reproducible framework that enables future systematic tests of morphology–dynamics relations within the PIUM context, without asserting observational validation at this stage. This study builds upon the foundational PIUM framework and should be interpreted as an intermediate step toward empirical testing rather than a final validation of the model.
Szabolcs Krehlik (Tue,) studied this question.