This work presents a standalone synthesis of the Twin Galaxy diagnostic, examining whether galaxies matched in present-day baryonic structure exhibit uniquely determined outer kinematic behavior. Combining a representation-aware identifiability constraint, a survey-scale empirical extension using HI kinematic models from the WALLABY Phase 2 Public Data Release, and morphology-conditioned twin diagnostics using MaNGA and Galaxy Zoo 2 data, the analysis demonstrates persistent non-uniqueness among disjoint baryon-matched (or HI-matched) galaxy pairs under admissible, metric-preserving summaries. At the same time, outer response structure remains systematically organized by morphology at the population level. The results are explicitly diagnostic and inferential: no new phenomenology or physical mechanisms are proposed, and the contribution is the formal delimitation of what outer kinematic tests can legitimately claim about identifiability and representation.
Jason Tramonti (2025) studied this question.