Scale Degeneracy and Its Resolution: The Route to Calibration-Free Absolute Quantification

<jats:p> Binding assays obey an equation of state from the canonical partition function, yet the term distinguishing total from free concentration has been underappreciated. Target-Capture Scaling (TCS) restores it: the master equation, parameterised by the dimensionless total feed ξ and the binding regime parameter κ (the unique pair forced by dimensional analysis), exposes scale degeneracy: an intrinsic symmetry under which concentration, capacity, and affinity cannot be individually resolved from a single equilibrium measurement. At  𝜅 → 0 the dissociation constant vanishes from the master equation; with digital readout, calibration-free absolute quantification becomes a structural consequence, not a statistical artefact.  governs the Fisher information geometry, kinetic relaxation, analog–digital complementarity, and variance partitioning (F <jats:sub>0</jats:sub> +F <jats:sub>1</jats:sub> =1), from the stoichiometric (𝜅 ≤ 0.1) to the thermodynamic (𝜅 ≥ 10) regime. Models across bioanalysis, pharmacology, enzyme kinetics, and environmental adsorption are -regime limits of the TCS master equation. Data spanning the  spectrum is consistent with the framework. </jats:p>