Flat and quasi-flat rotation curves of spiral galaxies are commonly interpreted as indicators of dynamical velocity equilibrium, often motivating mass-based explanations extending beyond the visible disk. Here we revisit this interpretation by reframing rotation-curve behavior as a structural projection problem grounded in observable spiral-arm geometry, stellar-density continuity, and kinematic organization. We develop an observationally anchored diagnostic framework operating directly on spiral-arm sequences extracted from face-on galaxy images. An index-based coordinate representation is used to evaluate geometric radius structure, velocity traces, and their differential relations locally along spiral arms without interpolation, smoothing, or model fitting. Internal structural–kinematic admissibility is tested using a Three-Module Diagnostic enforcing derivative continuity and chain-rule consistency, while external observational concordance is examined through a complementary Six-Pair Validation framework assessing cross-arm symmetry, bounded residuals relative to observed rotation curves, and density–gradient coupling. Applying this framework to NGC 628, NGC 1300, and IC 5332 reveals extended radial intervals in which spiral-arm geometry, stellar-density proxies, and velocity gradients evolve coherently under identical diagnostic criteria. Across all systems, quasi-flat rotation regimes coincide with admissible structural domains characterized by density plateaus, suppressed velocity-gradient fluctuations, and bounded observational residuals. The repeated appearance of stabilized velocity gradients along spiral-indexed coordinates indicates that large portions of spiral disks operate within structurally organized regimes of constrained kinematic variation. These results indicate that flat and quasi-flat rotation curves arise as observational projections of disk-wide structural coherence. This admissibility-based perspective provides a force-agnostic diagnostic reinterpretation of rotation-curve flattening complementary to conventional mass-centered approaches. This record includes the main manuscript and machine-readable supplementary Excel files supporting the diagnostic tables and panel analyses.
Youl Hour (Fri,) studied this question.