Topological Audio Fingerprinting via Hodge Decomposition

We present a topological audio fingerprinting method based on Hodge decomposition of audio signals. Given a signal W on a Riemannian manifold M, we decompose W = ∇φ + δψ + h, where h ∈ H¹(M,ℝ) is the harmonic component invariant under smooth deformations. The resulting 6-dimensional HodgeFingerprint achieves cosine similarity ≥ 0.96 for matched tracks and outperforms the Shazam baseline in 10/11 test cases. This preprint establishes prior art for topological audio identification via harmonic invariants.