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Shadow prices of connectivity are derived via the Feynman\u2013Kac representation, and open-loop solutions are refined with a machine learning controller. Methodologically, this integrates stochastic co-states with policy refinement for multilayer SES control. Conceptually, resilience is operationalized through network-level criteria. Numerical experiments under escalating drought show: (i) optimally configured controllers maintain strong resilience under moderate stress; (ii) beyond a critical drought threshold, only weak resilience is attainable; (iii) control effort exhibits layer asymmetry, with agri-food requiring sustained torque and biodiversity benefiting from punctuated interventions; and (iv) a governance wedge persists between technically cost-effective effort and stakeholders\u2019 willingness to implement it. 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