HodgeCodec

First audio codec based on Hodge decomposition and de Rham cohomology.

Theory

Any audio signal W decomposes into three orthogonal components:

W = ∇φ + δψ + h

• ∇φ — tonal/harmonic gradient (smooth, sustained tones)
• δψ — attack/transient coexact component
• h ∈ H¹(M,ℝ) — harmonic invariant (topological fingerprint)

The component h is invariant under pitch shifts, time stretching, and MP3 compression.

Results

• Cosine similarity ≥ 0.96 for matched tracks
• 10/11 wins vs Shazam baseline
• Training-free, O(N) time
• Implemented in open-source Rust

Preprint

Topological Audio Fingerprinting via Hodge Decomposition
Dyachenko, M. (2026). Zenodo.
DOI: 10.5281/zenodo.20618759

License

MIT © 2026 Maksym Dyachenko