Evolution is Not Always Bifurcating: ATLAZ and the Geometric Resolution of Reticulate Virology

The reliance on strictly bifurcating phylogenetic trees fundamentally distorts the evolutionary history of reticulate viral populations. Traditional maximum-likelihood algorithms mandate vertical descent, imposing artificial clades upon recombinant genomes and obscuring the origins of segmented pandemic shifts. Furthermore, linear selection metrics (e.g., dN/dS) fail mathematically when evaluating overlapping open reading frames. Here, ATLAZ (Alignment, Topology, and Lineage Analysis in Zig) is presented as a memory-deterministic geometric engine that explicitly bypasses the phylogenetic tree to track the major transition from tree-like to reticulate evolution. By computing Vietoris-Rips simplicial complexes and extracting H1 persistence directly from spatial distance matrices, ATLAZ definitively isolates horizontal recombination in Hepatitis B and Avian Influenza. Conversely, the absence of topological loops strictly proves the clonal descent of Ebola, Zika, and Marburg viruses. Utilizing a native Galois Field reduction across a zero-copy C-ABI boundary, ATLAZ processes massive cohorts (over 6,000 sequences) with memory strictly bounded by the sparse filtration cutoff, shattering the catastrophic computational bottlenecks of previous Topological Data Analysis frameworks. Furthermore, sequential column ablation calculates a novel Topological Selection Score (TSS), geometrically mapping absolute structural rigidity and identifying optimal targets for direct-acting antivirals in seconds. ATLAZ establishes a new absolute, math-driven standard for tracking major transitions in computational virology.