Topological structure of radiation-induced DNA damage encodes coupled LET-oxygen signatures

We present the first nuclear-scale persistent homology and Random Forest classification analysis of radiation-induced DNA double-strand break (DSB) topology across the clinical particle therapy range. Using TOPAS-nBio and the Voxel-Aware Oxygen model, we generated 2,450 simulated nuclei across 49 conditions (seven particle configurations, 0.2--70.7~keV/\textmu{}m; seven oxygen levels, 0.005--21\%~O$_2$) and extracted a 107-feature matrix across seven modalities. DSB topology encodes particle identity, Spread-Out Bragg Peak (SOBP) position, and oxygen tension in a three-tier hierarchy, with fidelity at each tier governed by the physical mechanism controlling it. Particle identity and SOBP position are exactly decodable (balanced accuracy = 1.000). Oxygen-level classification degrades monotonically with LET from 0.517 (electrons) to 0.189 (carbon distal SOBP), with a charge-driven non-monotonicity at the helium-to-carbon transition confirming that atomic number, not LET alone, governs topological discriminability. The joint 49-class task achieves balanced accuracy 0.346, seventeen times above chance. Per-class recall peaks universally at 0.5\%~O$_2$ (0.788--0.976 across all configurations), which is consistent with the OER curve inflection. Topological Summaries (persistent entropy, landscape integrals) dominate oxygen encoding at all LET ($\eta^2_{O_2} =\,$0.300--0.622). A partial-out test reveals two mechanistically separable channels: a count-mediated scale signal ($\eta^2_{O_2}$ survival ratio 0.062) and a count-independent shape signal preserved or enhanced in five of seven configurations (balanced accuracy survival ratio 1.011). Persistent entropy and landscape integrals, as novel radiobiological observables, provide a computational basis for characterizing oxygen-dependent damage topology in hypoxic tumor treatment planning.