Forecasting models for health-signal digital twins must preserve the oscillatory, frequency, phase, and state-transition dynamics of physiological signals, yet the pointwise metrics used to benchmark them cannot detect when these fundamental properties are lost. We show that this blind spot misranks models: across 11 architectures, models with comparable pointwise error diverge by up to 53° in phase accuracy, equivalent to roughly 123 ms for a 1.2 Hz cardiac rhythm and invisible to standard metrics. To enable development of models that escape such failures, we introduce TimeSynth, a controlled benchmarking framework with two reusable components: a physiologically grounded generator producing signals with analytically known ground-truth dynamics from parametric models fitted to real electroencephalography, electrocardiography and photoplethysmogram signals, along with diagnostics quantifying amplitude, frequency, phase, and state-transition fidelity. Linear and full-sequence attention models systematically lose frequency and phase information despite acceptable amplitude error, whereas architectures with localized temporal structure better preserve dynamical fidelity and adapt to observable state transitions; none, however, reliably preserves stochastic switching. Because the dominant determinant of fidelity is architectural, model choice becomes a principled, use-case-driven decision rather than a search for a single winner. TimeSynth thus supplies the controlled preclinical stress test missing before models are coupled to patient data, with a reusable generator and diagnostics for fidelity-aware development.

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