No Gradient, No Cluster: Feasibility of Single-Machine Discrete Topological Annealing for Structural Variant Path Inference in Graph Pangenomes

Graph pangenomes transform structural variations (SVs) from blind spots of linear references into computable graph-space objects. However, inferring a valid haplotype path among hundreds of spatially overlapping and topologically conflicting candidate edges is fundamentally a discrete combinatorial optimization problem. Current mainstream paradigms typically require GPU clusters, distributed memory, or platform-specific sequencing data, imposing a computational threshold that constitutes a hidden barrier to population-scale SV analysis. We propose and validate a path orthogonal to the calculus paradigm: Discrete Topological Annealing (DSA). DSA treats edge-set states on a breakpoint graph as search objects, generates neighborhoods via three discrete topological operators (Local Permutation, Segment Inversion, and Spatial Mutation), and drives convergence via the Metropolis criterion. On real VCF data from the 1000 Genomes Project Phase 3 chr22, DSA performs topological pruning of 300 real DEL/DUP/CNV records on an ordinary laptop without any third-party Python libraries: transfer entropy decreases from 6.3883 to 5.5294, retaining 58.7% of topologically compatible SV edges. To ensure evaluation integrity, we incorporate the Self-Certification Amplitude Δ as a built-in diagnostic panel (Δ = -0.0753, same-source mean 0.4383, cross-source mean 0.5136), indicating no same-source evaluation advantage. This paper demonstrates that when convergence dynamics come from statistical physics rather than the chain rule, a single laptop suffices for a principled global search, offering a deployable and auditable alternative for resource-constrained environments.