M30a The Complex HyperCore

M30a develops the Complex HyperCore by giving imaginary HC rank a precise interpretation: it is a Koenigs phase acting inside an étage, while cross-étage obstruction is measured by a Wronskian bracket. The central formula is exp (iT GR): u -> lambdaR^ (iT) u with generator GR = (ln lambdaR) u d/du in Koenigs-normalized coordinates. The paper identifies the branch microfibre with Koenigs monodromy: T = T*R kappa so imaginary rank T and branch address kappa are the same fibre coordinate in different normalizations. Its main structural result is the Wronskian bracket: GR, GS = (ln lambdaR) (ln lambdaS) W (fR, fS) d/dx which measures the failure of imaginary-rank flows at different étages to commute. M30a then interprets the cascade discrepancy as Wronskian holonomy and rewrites the fine-structure relation as: alpha^ (-1) = 1 / (LB^ (5/2) kappadisc) with kappadisc arising from the SC–TC cross-étage loop. Finally, the Drift Direction Conjecture is reformulated as a single commutator equation: GR, V = 0 inside one Koenigs chart, making the RH route more local and removing the earlier cross-étage transfer bottleneck