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Sustainability is now central to corporate legitimacy, yet its implementation remains uneven—particularly in emerging and fragile institutional contexts marked by weak enforcement, shifting stakeholder expectations, and fragmented governance. Although research acknowledges that senior executives shape sustainability outcomes, it often relies on structural or demographic proxies and overlooks how leaders actually interpret and address these demands. This conceptual, hypothesis-generating paper develops Executive Sustainability Cognition (ESC) as cognitive governance: the capability through which C-suite leaders select, frame, prioritise, and embed sustainability imperatives when formal institutional guidance is weak or ambiguous. Integrating Upper Echelons Theory, Institutional Theory, Stakeholder Theory, Strategic Leadership Theory, and sensemaking research, the paper proposes a four-stage ESC process: (1) attention and interpretation of sustainability cues, (2) framing and prioritisation of competing imperatives, (3) construction of sustainability vision, and (4) translation into structures, incentives, and culture. Eight testable hypotheses specify how ESC mediates between external pressures and organizational responses, and how institutional fragility, stakeholder fragmentation, and organisational learning orientation moderate these effects to produce symbolic versus substantive outcomes. By framing executive cognition as a substitute governance mechanism in fragile contexts, the paper offers a context-sensitive framework to guide research and improve sustainability practices in emerging and weak-governance markets.