Task geometry alignment enables parameter independent and accurate genomic search.

Standard sequence alignment models biological homology through the metric space of edit distance. While effective for global orthology, this rigid geometric assumption struggles with discrete biological realities-such as insertions/deletions (indels) and fragment-to-reference asymmetry-forcing a reliance on heuristic gap penalties. To address this, we propose Task-Geometry Alignment (TGA), a design principle that structurally aligns algorithmic representation with the intrinsic geometry of the biological task. We implement TGA in TGALIGN, an expert-parameter-independent tool that tiles reference databases to match query lengths, encodes sequences into gap-robust syncmer profiles, and indexes them for high-speed Approximate Nearest Neighbor (ANN) search. Benchmarking against leading aligners (USEARCH, VSEARCH, MMseqs2) demonstrates performance strictly bounded by biological architecture. On standard substitution-heavy markers (COI), TGAlign achieves statistical parity with the state-of-the-art. Conversely, on sequence fragments and indel-heavy markers, TGAlign yields statistically significant accuracy improvements (up to 10% on 16S) while matching the peak performance of MMseqs2 on highly variable ITS datasets. By translating sequence comparison into dense matrix operations via ANN indexing, the current implementation maintains sub-millisecond query latency-an order-of-magnitude reduction over traditional aligners-providing a robust and scalable framework for post-alignment genomic search. Source code is available at https://github.com/JustinBooneLab/TGAlign and datasets are archived at Zenodo (DOI: 10.5281/zenodo.17973054).