Space-Phase Memory at Cosmic Web Nodes: SP3 Deviations from Timescape Cosmology and a Strong-Lens Time-Delay Test

Timescape cosmology proposes that cosmic time is not globally uniform: clocks in voidsadvance faster than those in matter-rich regions due to cumulative gravitational timedilation in an inhomogeneous universe. SP3 (Space-Phase–Persistence–Pathway) theoryextends this picture by asserting that space itself is a conditionable medium whose prioruse by matter and energy leaves persistent, hysteretic structure. In this paper, we integratethese two perspectives and show that filament junctions (nodes) of the cosmic webrepresent a critical regime where SP3 predicts departures from Timescape’s averagedbehavior. We argue that nodes function as memory-saturated space-phase reservoirs,producing nonlinear, anisotropic, and history-dependent timing effects not captured bydensity-based models alone. Building on this conceptual framework, we design a concreteobservational test using strong-gravitational-lens time delays. The proposed test is framedas a null experiment within standard time-delay cosmography pipelines, asking whethernode-correlated residual delays persist after all conventional mass, shear, and line-ofsight corrections are applied. Detection of such residuals would indicate a non-geometric,history-dependent contribution to cosmic timekeeping consistent with SP3.