Unknot Linearization Redux for cyclic actions on the 4-sphere

Let $a4n$ act smoothly on $S^4$, and let $S$ be its fixed-point set, assumed to be an unknotted $2$-sphere. An equivariant bridge trisection is a bridge trisection preserved by the action, and its genus and bridge number are measured on the central surface and fixed set, respectively. Unknot Linearization Redux. $S$ admits a 1-bridge, genus-zero, equivariant bridge trisection. This is equivalent to the Unknot Linearization Conjecture: the remaining obstruction would be a nonlinear cyclic action fixing an unknotted sphere. The surrounding discussion explains that any counterexample must have equivariant trisection genus at least two, with the quotient either having larger bridge number or being exotic.