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Trustworthy artificial intelligence is frequently discussed through principles, performance measures, governance commitments, or general descriptors such as safe, fair, explainable, and responsible. These expressions are important but insufficient for determining whether a particular intelligent system is adequately justified for a defined use, environment, population, and decision context. This article proposes a conceptual AI assurance-case methodology for organizing trustworthiness reasoning through explicit assurance claims, decomposed subclaims, bounded acceptance criteria, evidence requirements, evidence-quality assessment, provenance, traceability, structured argumentation, defeater analysis, uncertainty, and residual-risk reasoning. The methodology responds to distinctive assurance challenges created by model opacity, distributional change, context dependency, conflicting trustworthiness objectives, incomplete evidence, human-oversight limitations, and lifecycle evolution. It distinguishes the existence of evidence from its relevance, validity, credibility, completeness, and sufficiency, while treating traceability as an aid to inspection rather than a guarantee of evidential quality. Structured arguments connect claims to evidence through warrants, assumptions, contextual conditions, and inference links, while counterevidence, argument gaps, evidence gaps, and unknown risks remain visible. Assurance cases may consequently support accountable deployment deliberation by clarifying decision gates, deployment boundaries, monitoring obligations, and conditions requiring reassessment. The principal contribution is an integrated methodology for constructing and maintaining bounded trustworthiness cases without treating assurance reasoning as proof of safety, fairness, legality, ethical sufficiency, compliance, certification, operational readiness, or deployment acceptability. The methodology supports transparent and challengeable reasoning, but requires domain-specific evaluation, governance review, stakeholder participation, and continuing lifecycle monitoring.