Rational design of nano-confined cobalt-based heterogeneous catalysts for peroxymonosulfate (PMS) activation remains challenging in Fenton-like systems, particularly in regulating interfacial electronic structures and establishing explicit electron transfer-activity correlations. To address this, we engineered a hierarchically structured Co@C-CNT composite featuring cobalt nanoparticles encapsulated in N-doped carbon polyhedrons interconnected by carbon nanotubes, forming a unique one-dimensional beads-on-string architecture. The strategic integration of CNTs significantly enhanced interfacial electron transfer kinetics, endowing the Co@C-CNT/PMS system with exceptional catalytic performance for carbamazepine degradation (k