A Topology-Driven Invariant Mass Kernel: Reference Implementation and Benchmark Against Atomic and Molecular Masses

This manuscript documents a canonical reference implementation of the Swirl--String Theory (SST) invariant mass kernel, as encoded in . The kernel maps a topological object $T$ (specified by braid index $b_T$, Seifert genus $g_T$, component count $n_T$, and a dimensionless total ropelength $L_{}(T)$) into an inertial mass $M(T)$ via a fixed, mode-independent functional. Three computation paths are supported: (strict evaluation with fixed quark-geometry factors), (single baryon-sector normalization fixed by the proton), and (analytic closure in which the proton and neutron are matched exactly without modifying the kernel). A semi-empirical nuclear binding correction is used to map nucleon-level predictions to atomic masses. In the mode (electron, proton, neutron exact by construction), the benchmark over elements H--U yields mean absolute percentage error ${$ with maximum absolute error ${$ for the fixed $(Z,N)$ table used.