ATLAZ Geometric Engine
TOPOLOGICAL DATA ANALYSIS
ATLAZ (Alignment, Topology, and Lineage Analysis in Zig) is a production-grade, memory-deterministic geometric engine acting as a topological subcomponent of the broader BioZig ecosystem.
Traditional phylogenetic algorithms force evolutionary history into strictly bifurcating trees. While this works for vertical descent, it fundamentally misrepresents reticulate evolution (e.g., recombination, reassortment, and horizontal gene transfer). ATLAZ resolves this by abandoning predefined graph structures entirely and instead utilizing Topological Data Analysis (TDA) and Persistent Homology.
Resolving the Bifurcation Constraint
EXACT HOMOLOGY LOOPS
Memory-Deterministic Vietoris-Rips
ATLAZ overcomes the catastrophic memory scaling (O(2^N)) of traditional TDA tools by leveraging BioZig's zero-copy C-ABI boundary and native Galois Field (GF(2)) matrix reductions. This enables the evaluation of topological features across multiple distance scales without triggering garbage collection overheads typical of Python or R implementations.
Identifying Reticulation
Within the ATLAZ engine, vertical clonal evolution is geometrically classified as zero-dimensional homology (H0). Conversely, reticulate evolutionary events—such as viral recombination—manifest mathematically as one-dimensional topological holes or loops (H1). ATLAZ precisely tracks the birth and death of these H1 features to map exact biological truth.