VDJ-KTS: A Formal and Probabilistic Framework for Verifying V(D)J Recombination Dynamics and Clonal Attractor Formation

This preprint introduces VDJ-KTS, a formal and probabilistic framework that models V(D)J recombination as a verifiable dynamical system rather than solely a sequence generator. The framework represents recombination as a probabilistic Kripke Transition System, enabling exact reasoning about reachability, termination, and pathological dynamical regimes under biologically grounded constraints. A central contribution is the Clonal Attractor Score (CAS), defined as the probability that recombination dynamics alone pre-configure a B-cell repertoire into a low-entropy clonal absorbing state. CAS does not model antigen-driven selection, somatic hypermutation, or microenvironmental expansion; instead, it quantifies a pre-selection susceptibility that constrains which clones can subsequently be stabilized and expanded once selection acts. All recombination parameters (segment usage, junctional insertions/deletions, retry behavior, accessibility priors) are inferred exclusively from nonproductive IGH rearrangements, ensuring that CAS reflects intrinsic recombination dynamics rather than antigenic or germinal-center selection. Productive rearrangements are used only for outcome labeling and validation. By separating recombination dynamics from downstream selection, VDJ-KTS provides a mechanistic prior on clonal sustainability and offers a formal bridge between molecular recombination mechanisms, dynamical systems theory, and clinically observed patterns of clonal dominance.