Paper B: Topological Charge Transport in the Holosphere Lattice A Defect Flux Law on Discrete Shells

This paper is the second in a four-part series (Papers A–D) that establishes the mathematical and physical foundations of Holosphere Theory. Paper A introduced the vacancy scaling law, showing that the cumulative number of missing sites on quasi-radial shells grows with surface area but includes an O(1) per-shell correction. Paper B develops the topological origin of these corrections by deriving a flux balance law for disclination transport. Each shell of the Holosphere lattice carries a net disclination charge Q_k = 12, as required by the discrete Gauss–Bonnet theorem. These disclinations form scar networks that either propagate coherently between shells or rearrange locally. We capture this process in the equation Delta_k = B_k + epsilon_k where Delta_k is the vacancy anomaly, B_k is the net boundary flux between shells, and epsilon_k is an intra-shell drift term representing local rearrangement. This relation shows that the vacancy anomalies of Paper A are not arbitrary, but arise from a deeper conservation principle. A numerical experiment using a cuboctahedral (FCC-like) lattice validates the theory. The simulation identifies disclinations directly from geometry, bins them into shells, and computes Delta_k, B_k, and epsilon_k. The results confirm that Delta_k remains bounded, B_k is divergence-free, and epsilon_k averages to zero with bounded variance. These findings demonstrate that the flux–drift law is both mathematically consistent and empirically observable. Together, Papers A and B establish that vacancy scaling and defect transport are two sides of the same phenomenon: global site-count deficits emerge from local topological charge conservation. Paper C will extend the framework to energetics and entropy, while Paper D will calibrate the model to physical constants, completing the series.