The Erdős–Straus decomposition reveals a harmonic substructure when interpreted through modular resonance. The reciprocal terms behave like interacting frequencies constrained by arithmetic curvature.

Each admissible triple corresponds to a stable resonance configuration within a modular field.

Bernoulli numbers act as phase regulators governing curvature decay across modular lifts.

Their structure encodes frequency attenuation and harmonic signature.

Modular residue classes interact as resonance bands, producing interference patterns across congruence strata.

Result: a harmonic lattice whose density varies predictably with prime factorization.

Faulhaber sums introduce braid-like constraints across p-adic modular space, ensuring global coverage without redundancy.