One Residual Law for Quantum, Thermodynamic, and Gravitational Equilibria: A DSFL Framework in One Calibrated Hilbert Space

We formulate a single, sector–neutral Lyapunov law that treats quantum mechanics, thermodynamics, and general relativity as three calibrations of one underlying feedback structure. The basic data are a shared Hilbert space, a blueprint space of statistical degrees of freedom, a physical space of realised degrees of freedom, and a calibration map between them. Their mismatch is quantified by one quadratic residual of sameness in a fixed instrument norm. Admissible evolutions are those that preserve calibration and are nonexpansive in this norm; for such evolutions we prove a data–processing inequality for the residual, a Lyapunov inequality with an intrinsic DSFL clock, and a cone–type locality condition. We then build explicit quantum, thermodynamic, and gravitational calibrations and show that their sectoral residuals add to a single global residual whose decay rate is controlled by the slowest sector. In this picture, collapse, entropy production, and curvature–matter balance become three faces of the same residual–driven attractor. A UV master inequality explains how scale–resolved models fit into one global DSFL law, and simple model worlds (qubit channels, Markov chains, QNM–like modes, and a Bell/CHSH sector) illustrate how standard phenomena such as Born statistics, ringdown, and Tsirelson–saturating nonlocality can all be read as structural consequences of one calibrated residual in one Hilbert space.