TCP-BioSync: A Unified Framework for Continuous Quantification of Biological Age through Ontological Binding of Molecular Diagnostics and Digital Physiology

"Supplementary Material S1: Python reference implementation" Background. Human biological aging evolves continuously, yet its clinical measurement remains confined to discrete snapshots — annual diagnostics, occasional epigenetic clock assays — separated by months or years. This temporal granularity is incompatible with the emerging need to monitor the response to geroprotective interventions on a daily basis. Objective. To establish a unified mathematical and computational framework that binds clinical-grade molecular diagnostics with consumer-grade continuous physiological signals, producing a medically defensible, high-temporal-resolution estimate of biological age and its rate of change. Methods. We introduce TCP-BioSync, comprising (i) a three-axis data schema uniting six chronic-disease PCR markers, six reverse-aging PCR markers, and five continuous smartphone-derived physiological signals (remote photoplethysmography [rPPG], heart rate variability [HRV], inertial gait symmetry, sleep quality, activity); (ii) an ontological binding operator ⊗ that combines static molecular baselines with dynamic modulators under a monotonicity-preserving formalism; (iii) three synchronization engines yielding the Metabolic Energy Live Index (MELI), the Real-time Inflammaging Index (RIAI), and Live ΔmAge — a continuous extension of Horvath-type epigenetic clocks; and (iv) a SHA-256 hash-chain integrity layer (Trust Code Package, TCP) conferring medical-record–grade evidentiary weight on the resulting biomarker stream. Results. A reference Python implementation reproduces all four mathematical primitives. In a 60-sample synthetic simulation, the three engines exhibit stable numerical behaviour (E_live variance < 1.5 after exponential moving-average smoothing), correctly flag cardiovascular high-risk windows under transient LF/HF elevation, and accumulate sub-second ΔmAge updates at 10⁻⁶-year resolution. Hash-chain integrity was verified across 61 records. Conclusions. TCP-BioSync provides the first operationally defined framework under which intermittent molecular diagnostics and continuous digital physiology yield a single, legally admissible, time-resolved trajectory of biological age. The framework is designed to be falsifiable through a two-phase clinical programme and establishes a foundational platform for precision geroscience. Keywords reverse aging; epigenetic clock; digital biomarkers; remote photoplethysmography; heart rate variability; hallmarks of aging; ontological binding; computational geroscience; Horvath clock; hash-chain integrity; precision medicine.