TCR-FramePose: a local-frame representation for decomposing global docking and CDR3 loop geometry in TCR-pMHC recognition

T cell receptor recognition of peptide-MHC depends on sequence, interface chemistry, and three-dimensional geometry, but docking geometry is often summarized at the whole-receptor level, leaving CDR3-local pose difficult to compare across structures. We introduce TCR-FramePose, a local-frame descriptor set that represents each TCR-pMHC complex as three bodies - whole TCR, CDR3a, and CDR3b - measured relative to a pMHC groove frame. For each body, FramePose decomposes the native pose into reach, offset direction on S^2, and orientation on SO(3); for tangent-space analyses, these components are mapped to six coordinates per body and 18 coordinates per complex. Applied to 378 curated abTCR-pMHC crystal structures, FramePose recovers known class-associated receptor-placement differences and additionally resolved whole-TCR and CDR3b orientation shifts that were not captured by crossing angle. The same orientation coordinates identified reverse-polarity and off-axis outliers as distinct modes. In cross-validated association analyses, FramePose added nonredundant BSA- and affinity-associated information beyond conventional descriptors, and the modest affinity gain was concentrated in CDR3 orientation blocks which were least recoverable from conventional descriptors. Biological grouping analyses showed that shared receptor pose over peptide-MHC was organized primarily by germline V-region framework. TCRs recognizing the same peptide-MHC target favors shared FramePose geometries rather than strong receptor-specific divergence, whereas CDR3 sequence did not detectably reposition the rigid-body pose after antigen context and germline framework were fixed. MHC allele and peptide length contributed smaller adjustments, localized mainly to CDR3b and groove-normal orientation axes. Finally, interface analyses showed that affinity tracked interface burial, with CDR3b reach linking FramePose geometry to binding through buried surface area. Within engineered panels, mutation-level effects were panel-specific, with CDR3b remodeling localizing to a recurrent interface region but varying in direction across receptors. These properties enable FramePose to serve as a geometric filter for in silico TCR-pMHC models and as a feature layer for structure-guided TCR engineering. Together, TCR-FramePose provides a nonredundant geometric layer for structure-guided TCR-pMHC analysis, linking germline-scaffolded recognition, CDR3-local pose, and interface organization without replacing sequence, contact, or energetic descriptors.