The adoption of generative AI in software-intensive systems is proceeding rapidly, but current analytical instruments - principally unidimensional maturity models - compress important configurational variation into a single progressive axis. Drawing on an inductive interview study of eighteen senior practitioners across telecommunications, automotive, defence, aviation, banking, energy, government, and enterprise software services, this paper presents the Trustworthy Autonomy Health Check Model: a structured, multidimensional instrument for characterizing how organizations establish trust in GenAI-assisted software engineering. The model organizes eight empirically grounded dimensions into a system layer (Scope of Agent Authority, Assurance Mechanisms, Data Trustworthiness, Architectural Containment, Traceability & Comprehensibility) and an organizational layer (Governance, Human Oversight Posture, Workforce Capability Sustainability), each on a five-level ordinal scale. A cross-cutting overlay of four trust paradigms - operational, engineering, statistical, and containment-based - captures how trust is established, complementing the dimensions capturing what must be trustworthy. The model is diagnostic rather than prescriptive: it supports cross-organizational comparison, surfaces configurational trade-offs, and locates an organization in a shared space without imposing a single progression path. Higher levels are not inherently better; the goal is alignment across dimensions appropriate to the organization's domain and chosen trust paradigm. This is formalized as the alignment hypothesis: effective trustworthiness is constrained by the fit between the scope of agent authority and the dimensions enabling it, with misalignment producing pathological risk or unnecessary friction. We discuss how practitioners can apply the model and outline directions for empirical validation.

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