The Modal Triplet Theory Program B4: Encoding Intersections and Structural Rigidity

We analyze the simultaneous coexistence of gravity, gauge structure, and quantization encodings within Modal Triplet Theory. We show that triple-compatible encoding frameworks are generically rigid: small deformations typically destroy admissibility or consistency. This rigidity is structural rather than dynamical and arises from the independent constraints imposed by circle, lens, and nil obstructions. We interpret the Standard Model as an isolated encoding intersection rather than a fundamental or unique theory. Anomaly cancellation and representation constraints are reinterpreted as admissibility conditions rather than quantum accidents. The results explain why certain effective theories are highly constrained without deriving specific parameters.