The mechanism which 'adapts' the T-cell antigen receptor (TCR) repertoire within a given major histocompatibility complex (MHC; HLA, in humans) genotype is essential for protection against rapidly dividing pathogens. Historically attributed to relative affinity, genetically vast TCRs are surprisingly "focused" towards a micromolar affinity for their respective pHLA ligands. Thus, the somatic diversity of the TCR with respect to MHC restriction, and (ultimately) to pathogens, remains enigmatic. Here, we derive a triple integral equation (from fixed geometry) for any given V-domain in TCR bound to pMHC. We examined solved complexes involving HLA-DR and HLA-DQ, where all the available structures are still reasonably analysed. Certain V-beta domains displayed "rare" geometry within this panelspecifying a very low ("highly-restricted") rotational probability/volumetric density (dV). Remarkably, hydrogen (H)-bond charge-relays spanning CDR3-beta, the peptide, and polymorphic MHC distinguished these structures from the others; suggesting that CDR3 binding chemistry dictates CDR2 'scanning' on the respective MHC-II alpha-helix. Taken together, this analysis (n = 38 V-domains) supports a novel geometric theory for MHC restriction-one not constrained by a thymus "optimized" TCR-affinity.