A Minimal Hypercharge Bridge in ECSM: From Closure-Active SU(2)L to Emergent Electric Charge

This paper presents a notebook-backed algebraic test of the next weak-sector bridge in the Emergent Condensate Superfluid Medium (ECSM) framework. Previous ECSM work established a closure-active neutral-charged weak pair, Ψ_L^ECSM = (Q_0, Q_ch)_L, and showed that this pair admits a minimal SU(2)_L-like algebra, with T_3 assigning opposite branch labels: T_3(Q_0) = +1/2 T_3(Q_ch) = -1/2 The present paper tests whether a minimal U(1)-like branch-phase or hypercharge label Y can recover the neutral/charged electric-charge split through the standard electroweak-like combination: Q_ECSM = T_3 + Y/2 A notebook-backed calculation shows that the left-active doublet assignment Y_L = -1 gives Q(Q_0) = 0 Q(Q_ch) = -1 A direct scan over Y finds the exact best value Y = -1.0 with target error 0.0. The right-handed charged branch is consistently represented as an SU(2)_L-singlet with T_3 = 0 Y_R = -2 Q = -1 while a possible right-handed neutral closure singlet or sterile-like candidate has T_3 = 0 Y_R = 0 Q = 0 A finite-response deformation test replaces the coherent generator T_3 with T_3(χ) = χT_3 + (1 - χ)ΔT_3 For a generic deformation, the electric-charge split drifts away from the target values at χ < 1, while the exact neutral/charged split is recovered at χ = 1. The final notebook verdict is: PASS_MINIMAL_HYPERCHARGE_ELECTRIC_CHARGE_BRIDGE This paper does not derive the full electroweak theory, Weinberg angle, W/Z masses, gauge coupling values, Yukawa couplings, anomaly cancellation, hypercharge quantisation, or precision weak observables. Its purpose is narrower: to establish that the ECSM closure-active SU(2)_L-like doublet can be supplemented by a minimal U(1)-like label so that the neutral and charged branches recover the correct lepton-like electric-charge split.