τ Biology: Internal time reparameterization as a universal compression operator for growth, aging and hazard heterogeneity

Biological trajectories that appear heterogeneous under chronological time often share a simpler law when expressed in an internal progress coordinate τ. This paper formalizes τ Biology as a reparameterization framework that replaces external clock time t with an intrinsic internal time τ and an associated clock rate field χ. We show that a wide class of growth laws collapse across individuals and environments when mapped from t to τ. We derive the exact transformation between internal hazard and chronological hazard and show how variability in χ induces apparent frailty and dispersion in lifespan without adding biological parameters to h(τ). We propose a quantitative success metric, the collapse gain G, and provide an open reproducible Python implementation for deterministic in silico validation and for semi-synthetic stress testing under measurement noise and irregular sampling. Finally, we define concrete Level 3 validation targets using NHANES and UK Biobank aging cohorts and epigenetic clock trajectories, as well as Drosophila and Arabidopsis benchmark datasets to evaluate collapse and hazard mapping under controlled heterogeneity. Preliminary analyses on NHANES and UK Biobank cohorts show collapse gain G > 2.5, supporting feasibility of Level 3 validation.