This record contains version 1. 2 of the Upsilon Signature work, presented as a revised and expanded standalone article. Compared with version 1. 1, the scope has been narrowed and clarified: the paper focuses on line-of-sight velocity-dispersion profiles, σLOS (R), in globular clusters, core-collapsed globular clusters, and elliptical galaxies. Version 1. 2 also expands the observational sample, distinguishes object classes more explicitly, introduces a more detailed parameterization protocol, and adds robustness and sensitivity tests designed to assess whether the diagnostic agreement degrades when the main assumptions of the framework are deliberately altered. The extension to spiral galaxies, previously treated as part of the broader development, is retained only as an outlook and left for separate treatment. The work presents the Upsilon signature (ϒ) as both a physical hypothesis and an operational diagnostic framework for interpreting σLOS (R) profiles in dispersion-supported stellar systems. The framework rests on two linked assumptions: first, that the observed profile samples an effective frontal mass column ϒ along the line of sight rather than the full system diameter; and second, that the orbital families contributing to the observable are preferentially populated from birth conditions near apocenter. Combined with a spherical reference density profile and a projected Keplerian kernel, these assumptions generate a family of theoretical dispersion curves σₜh (R, e), parameterized by effective eccentricity e. The resulting template predicts a localized diagnostic feature around the transition between the untruncated and truncated regimes, expressed as a valley or hump and, more specifically, as a narrowing or “neck” where the theoretical families converge. Applications to globular clusters, core-collapsed globular clusters, and elliptical galaxies, together with the robustness and sensitivity tests included in this version, indicate that, within the analyzed sample, the observed σLOS (R) profiles constrain the allowed region of the template and permit an operational inference of the dominant orbital geometry in the form of an effective eccentricity eₑff (R). The numbering of several equations is retained from the related plotting-software documentation for traceability. This version should therefore be read as a self-contained article linked to the associated software and data records, while preserving formal continuity with the previous Upsilon Signature documentation. As a preprint, this work is made openly available to facilitate scientific discussion, critical review, and independent assessment of the proposed hypothesis, methodology, software-linked formulation, and observational interpretation. It should be understood as a consolidated and citable version of the framework, while remaining open to comments, corrections, alternative interpretations, and further observational tests.
José Manuel Girón Díaz (Wed,) studied this question.