When Strong Hα Profile Preferences Fail: A Cohort-Level Robustness Audit in Little Red Dots

We present a cohort-level robustness audit of broad Hα profile inference in a predefined sample of 31 spectroscopically confirmed RUBIES Little Red Dots. The analysis tests optimizer and parameter-bound dependence, symmetric nuisance-absorber specification, candidate-set dependence, absolute-fit adequacy, and conditional covariance sensitivity. Under the inherited nuisance specification, three sources initially satisfied |D| > 10 for the two-Gaussian versus scattering-shaped comparison; after widened-bound deterministic multistart fitting, none did. A controlled intervention in UDS_167741 identifies an active parameter bound as the dominant cause of a formally converged but grossly inferior minimum. Across 775 covariance-conditional fits, 28 of 31 objects change at least one of profile ranking, pairwise status/sign, or nominal adequacy. The main conclusion is methodological: strong Hα profile preference is not equivalent to unique physical mechanism identification. Black-hole mass estimates that depend on the broadening mechanism should remain model-conditional until calibrated covariance and independent physical discriminators are available. The accompanying reproducibility archive contains the verified numerical audits, public spectral inputs, reconstructed catalogue, optimizer diagnostics, covariance sensitivity results, analytical code, numerical results, SHA-256 manifests, and machine-readable outputs used in the study.