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essential simplices 1graph theory 1harmonic cycles 1one-dimensional bars 1persistent homology 1

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math.AT2026

Essential Simplices Dominate in Harmonic Representatives of One-Dimensional Persistent Classes

Saugata Basu, Aldo Guzmán-Sáenz, Laxmi Parida

The paper proves that for generic one‑dimensional persistent homology classes, harmonic cycle representatives give strictly larger (in absolute value) coefficients to essential edg…