The τ₀ Theorem and the Birth of Metascience

Living systems across molecular, neural, and behavioral domains universally exhibit saturating stimulus–response functions. We demonstrate that when three fundamental constraints are imposed—(i) thermodynamic energy limitation, (ii) information-processing latency, and (iii) control-theoretic stability—the response functions of such systems necessarily converge to a low-order rational form. This mathematical family, typified by $S(\tau) = S_c \tau / (\tau_0 + \tau)$ or its dimensionless variant $\hat{S}(\hat{\tau}) = \hat{\tau} / (\hat{\tau}_0 + \hat{\tau})$, subsumes classic models such as Michaelis-Menten kinetics, neural spike responses, and temporal discounting in behavior.We further show that these rational forms arise as unique solutions under delayed dissipation and predictive coding constraints, and contrast them with exponential, linear, and sigmoid alternatives which violate one or more physical principles. The theory is validated across canonical data from enzyme kinetics, perceptual psychophysics, and decision-making systems. Strikingly, the same response structure applies to the knowledge-generation process of science itself. Theory formation, replication dynamics, and citation diffusion can each be modeled as constrained response processes within this saturating grammar. Hence, science enters a state of formal reflexivity: its own structure can be captured by the universal modeling framework it helped to construct. This marks the emergence of meta-science—not as a philosophical abstraction, but as a quantitatively grounded consequence of a deeper law uniting life, matter, and knowledge.