A Framed Three-Strand Topological Information Model: Exact Charge Mapping, a Bilinear Mass Constraint, and a Finite Residual Vacuum Sector

We present a discrete kinematic model built from the three-strand braid group B3 witha local slot-based framed-transfer rule. The model cleanly separates coarse closure topology from path-dependent framed memory, allowing macroscopically trivial closures to re-tain quantized internal residual structure. A computational sweep over 118,096 admissiblebraid histories conrms large-scale topology framing decoupling. Using a universal closure-scaled framing map, we show that the first-generation electroweak quantum numbers are reproduced exactly by linear functionals on the framing vector. We then define a bilinearvacuum-mass functional from a rank-two vacuum tensor acting on left/right framed data.The first-generation mass-area matrices satisfy the exact algebraic identity Mu = Md+3 Me,which holds unconditionally for any vacuum tensor K and implies the rigorous bound|mu−md| ≤ me on bare kinematic masses. Finally, we observe that residual framed memoryin the topological identity sector provides a natural finite mechanism for nonzero vacuum energy density. The paper is scoped as a kinematic-combinatorial framework: exact algebraic identities are proved inside the model, while larger physical mass splittings and radiative structure are attributed to dynamical dressing beyond pure topology.