SubmissionNumber#=%=#12 FinalPaperTitle#=%=#Geometric Separation Without Functional Specialization: Auditing Subspace Disentanglement in Dual-Encoder LLM Paraphrase Detection ShortPaperTitle#=%=# NumberOfPages#=%=#6 CopyrightSigned#=%=#Govind Arun JobTitle#==# Organization#==# Abstract#==#Explicit subspace disentanglement, enforcing orthogonality and simplex constraints on learned projections, is an increasingly common recipe for paraphrase models claimed to separate lexical, syntactic, and semantic information. A dual-encoder hierarchical model trained with these constraints on the DiPPer corpus of LLM-generated paraphrases produces near-perfect geometric separation, a pairwise Centered Kernel Alignment (CKA) of roughly $0.0007$, yet that separation is not evidence of functional linguistic specialization. Three results establish this. First, near-zero CKA is largely preordained by an explicit orthogonality penalty, which converges to $4\times10^{-6}$. Second, each of the three subspaces, including the nominally syntactic one for which we identify no functional probe, classifies paraphrase in isolation at $F_1$ above $0.986$, so the subspaces are not functionally distinct. Third, removing disentanglement at matched capacity costs only $0.013$ $F_1$, leaving most of the reported gain attributable to dual-encoder capacity rather than disentanglement. Capacity-matched ablations and controlled functional probes, not CKA alone, are required to substantiate disentanglement claims; orthogonality penalties otherwise manufacture the very metric used to certify them. Author{1}{Firstname}#=%=#Govind Author{1}{Lastname}#=%=#Arun Author{1}{Username}#=%=#govind02 Author{1}{Orcid}#=%=# Author{1}{Email}#=%=#govind123.ga@gmail.com Author{1}{Affiliation}#=%=#University of Maryland, College Park Author{2}{Firstname}#=%=#Ashish Anton Author{2}{Lastname}#=%=#Abraham Author{2}{Username}#=%=#ashishabraham Author{2}{Orcid}#=%=# Author{2}{Email}#=%=#ashishabraham22@gmail.com Author{2}{Affiliation}#=%=#College of Engineering Trivandrum Author{3}{Firstname}#=%=#Gadha Lekshmi Author{3}{Lastname}#=%=#P Author{3}{Username}#=%=#gadhalekshmip Author{3}{Orcid}#=%=#https://orcid.org/0009-0006-4741-7286 Author{3}{Email}#=%=#gadhalekshmip@gmail.com Author{3}{Affiliation}#=%=#Rutgers ========== èéáğö