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A clinically actionable Cardiac Digital Twin (CDT) should reconstruct individualised cardiac anatomy and physiology, update its internal state from multimodal signals, and enable a broad range of downstream simulations beyond isolated tasks. However, existing CDT frameworks remain limited to task-specific predictors rather than building a patient-specific, manipulable virtual heart. In this work, we introduce Chain of Flow (COF), a foundational ECG-driven generative framework that reconstructs full 4D cardiac structure and motion from a single cardiac cycle. The method integrates cine-CMR and 12-lead ECG during training to learn a unified representation of cardiac geometry, electrophysiology, and motion dynamics. We evaluate Chain of Flow on diverse cohorts and demonstrate accurate recovery of cardiac anatomy, chamber-wise function, and dynamic motion patterns. The reconstructed 4D hearts further support downstream CDT tasks such as volumetry, regional function analysis, and virtual cine synthesis. By enabling full 4D organ reconstruction directly from ECG, COF transforms cardiac digital twins from narrow predictive models into fully generative, patient-specific virtual hearts. Code will be released after review.