Unifying liquid water anomalies through a protonic pseudospinor order parameter

Introduction: Liquid water exhibits correlated density, thermodynamic, dielectric, transport, structural, and phase-boundary anomalies that are commonly described by separate phenomenological variables. This work asks whether a single internal protonic order parameter can provide a common parent architecture for the broader anomaly landscape. Materials and methods: A local hydrogen-bond unit is represented by the direct product of left/right proton localization and a binary torsional-sign sector, giving a four-component internal protonic pseudospinor. Its bilinear projections define torsional, tetrahedral/crystallinity, and polarization sectors, which are coupled to the hydrodynamic density deviation. These fields enter a Landau–Ginzburg effective Hamiltonian with density–torsion, torsion–crystallinity, and torsion–polarization couplings. The observed equation-of-state density stiffness is distinguished from the bare coefficient of the coupled fluctuation Hamiltonian, and the torsional crossover is rounded at the finite coarse-graining resolution so that its susceptibility remains finite. Results: The calculations provide sector-level comparisons rather than an independent validation of a common mediator. Density and compressibility are equation-of-state calibration anchors; heat capacity is evaluated with the prescribed rounded torsional stiffness; the broadband dielectric spectra are normalized to the measured 10 GHz loss and use stated temperature-specific composite relaxation times; the isotope-derived memory increment is transferred to viscosity; and the phase branch is a calibrated boundary proxy. Eliminating the centered torsional fluctuation nevertheless derives a rank-one coupling matrix in which density–crystallinity, density–polarization, and crystallinity–polarization cross-responses would share χ q ( T ) = a q ( T ) − 1 . No direct mixed cross-response dataset is used here to test that prediction. Conclusions: The protonic pseudospinor is proposed as an auditable organizing architecture for correlated liquid-water anomalies. Its common four-state origin, bounded admissible state space, and factorized q-mediated coupling structure are the principal theoretical contributions. The rank-one shared-q response is a falsifiable prediction, not a validation established by the present sector-level comparisons. Independent evaluation requires a fully numerical prespecified q-sector and response maps, joint estimation, and held-out measurements of mixed density–polarization, density–crystallinity, or crystallinity–polarization responses.