Deriving a Hypercharge-Like Branch Phase from ECSM Closure Constraints: Neutral-Charged Charge Recovery Beyond Assigned Y

This paper derives a minimal hypercharge-like branch phase from ECSM closure constraints. Starting from a previously derived two-branch closure-active algebra with T3(Q0)=+1/2 and T3(Qch)=-1/2, and imposing the required neutral and charged branch charges Q(Q0)=0 and Q(Qch)=-1, the common left-active branch phase is fixed uniquely as YL=-1. Singlet-like branch phases then follow from T3=0, giving Y=-2 for the charged singlet branch and Y=0 for the neutral closure singlet. The companion notebook verifies the derivation, performs a scan over Y, identifies YL=-1 as the unique zero-error solution, derives the singlet values, and confirms coherent-limit recovery under a finite-response deformation. The result does not claim a full derivation of Standard Model hypercharge quantisation, anomaly cancellation, coupling values, the Higgs mechanism, or precision electroweak observables. Its narrower claim is that, within the ECSM weak-sector bridge, once the two-branch closure algebra has derived the T3 labels, the minimal hypercharge-like branch phases required for neutral-charged charge recovery are no longer arbitrary assignments.