Spinorial Sheet Transport in the Fibonacci–Mellin Transform: SU(2) Connection, Hopf Holonomy, and Global Incommensurability

The Fibonacci–Mellin transform is a finite Vandermonde analysis bank on a multiplicative golden lattice whose ten rows split into five channel pairs, the two members of a pair differing by a deterministic phase twiddle. This paper determines the transport generated by the family of local cells attached to a pair: an exact rotation about a single axis, obeying a cocycle law with a sample-independent increment, so each branch carries a discrete SU(2) connection with one generator. The normalised state lies on S³, its Stokes image traces an equator of S², and the horizontal lift of the canonical Hopf connection returns to minus itself after a relative phase 2π and to itself after 4π. Two global results follow: one N-step advance of the scale cell is not a holonomy loop, and no non-zero parameter closes the five pairs simultaneously, because consecutive rates stand in the irrational ratio φ^(1/5). The bundle carries a deterministic suite of twenty-five checks, each paired with a corruption that must make it fail, and a script binding every quoted number to the record.