Gauge Rigidity and Holonomy Classification of Time-Scaled Intertwining Cocycles on Hilbert Bundles

We extend the discrete gauge rigidity of time-scaled intertwining cocycles to operator networks over a connected manifold M and classify the holonomy that the continuous setting admits. For dissipative semigroups $S_x(t)=e^{-tA_x}$ linked by transport operators $K_γS_{γ(0)}(t)=S_{γ(1)}(λ(γ)t)K_γ$ al