HγC P1: Bounded Comparison between Track A Galactic Closure and Projected-Profile Morphology in the HγC Framework

This paper establishes the first controlled comparison interface between the bounded Track A galactic object and the projected-profile morphology object of the Track B branch in the HγC framework. HγC O6 established that the Track A galactic line has reached bounded closure in restricted form, while earlier weak-field geometric and projected-profile work showed that weak-field lensing observables should be interpreted as probes of projected accumulation geometry rather than as direct tracers of instantaneous baryonic structure. P1 takes the next justified step by asking how the bounded Track A object should first be related to the Track B projected-profile morphology object. The answer proposed here is deliberately bounded: the relation should not yet be read as full branch integration, but as bounded comparison organized through support-bearing correspondence, projection-conditioned residue, and branch-sensitive tension. Within this framework, the strongest directions of the bounded Track A object, especially breadth, organized localization, and persistence-bearing morphology, carry forward positively into the projected-profile branch under transformed observational conditions. Part of the remaining openness is re-read as projection-conditioned residue generated by projection, profile development, redistribution, and finite relaxation. Remaining differences are treated as branch-sensitive tension: typed and localized limits of cross-branch continuity that remain compatible with bounded comparison so long as they do not proliferate into the support-bearing comparison core. The scope of the paper is deliberately limited. P1 does not attempt full branch integration, precision reconstruction of observed lensing systems, unique mapping from galactic residual morphology to projected accumulation geometry, temporal W-series reorganization, or full relativistic completion. Instead, it establishes bounded comparison as the first post-O-line comparison interface between Track A galactic closure and Track B projected-profile morphology.