Electromagnetic Helicity and Chern–Simons Structure in Modal Triplet Theory

We formulate electromagnetic helicity and Chern–Simons structure within the coherent sector of Modal Triplet Theory (MTT). The physically relevant electromagnetic field is defined on a finite-rank coherent bundle selected by a spectral projector that varies over spacetime. This variation induces additional geometric (Berry-type) terms in the effective connection, which must be included for correct curvature and conservation laws. We define coherent-sector helicity and a properly normalized Chern–Simons functional, and derive exact balance laws with explicit remainder terms controlled by the variation of the coherent projector. Using standard spectral-gap and Riesz-projector estimates, we show that these remainders are bounded on admissible spacetime slabs. As a result, electromagnetic helicity and Chern–Simons structure are well defined and approximately conserved whenever coherence admissibility holds, while controlled violations occur when admissibility breaks down. The framework clarifies how topological electromagnetic invariants arise as effective, admissibility-conditioned quantities rather than as globally protected topological charges.