Complex systems comprise heterogeneous domains whose states, uncertainties, risks, and control consequences can cross domain boundaries. Existing cross-domain digital twin approaches broadly focus on comparison, reuse, semantic mapping, standardization, and interoperability, but do not inherently require operational connections among domain states, errors, objectives, constraints, decisions, and controls. This article proposes the trans-domain digital twin as an operational formulation along the continuum of Composite/Federated Digital Twin Systems. This approach connects heterogeneous domain twins through an aligned shared state, explicit coupling of data, models, states, errors, objectives, and controls, heterogeneous temporal coordination, joint decision-making, and feedback-based adaptation. The proposed framework presents a seven-layer conceptual architecture, a trans-domain orchestration core, minimum compliance conditions, a general operational formalism, progressive fast-meso-slow loops, and a single-episode offline training mechanism linked to bounded online adaptation. It also describes conceptual validation and evaluation criteria, a maturity model, a reference deployment architecture, and requirements for runtime safety, provenance, versioning, and model lifecycle management. The framework is conceptually mappable to standards for digital twins, model exchange, distributed simulation, and smart transducers; however, its formal compliance and operational effectiveness must be examined through independent benchmarks, uncertainty quantification, ablation testing, and field validation.

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