A Scientific Proposal: The Law Of Harmonic Phase-Lag Integration as a Structural Constraint in Cosmological Observation

This work proposes the Law of Harmonic Phase-Lag Integration (HPLI) as a structural constraint on physical observation in cosmology and astrophysics. The central claim is that all observational data represent time-integrated, phase-lagged responses to evolving physical systems, imposed by finite signal propagation, detector response, and reconstruction processes. As a result, no observation corresponds to an instantaneous system state. Rather than introducing new particles, forces, or modifications to existing physical laws, HPLI constrains how established physics may lawfully appear through observation. The framework demonstrates that many widely discussed observational discrepancies—such as exoplanet parameter divergence across detection methods, gravitational lensing mass excess, rapid early black hole growth, and gravitational-wave–electromagnetic timing offsets—arise naturally when instantaneous-state assumptions are applied to temporally integrated measurements. The paper provides: A formal mathematical formulation of phase-lag integration, A minimal, law-centric visual framework, Representative observational case studies across multiple astrophysical domains, Explicit falsifiability criteria and experimental test pathways, Clear boundary conditions and known limitations. HPLI preserves conservation laws and relativistic causality, reframing apparent anomalies as lawful consequences of observational structure rather than indicators of theoretical failure. Within the broader CAT-12 framework, the law motivates corresponding constraints on inference while remaining conservative, testable, and compatible with standard cosmology. This work is intended for researchers in cosmology, astrophysics, and observational inference, particularly those working with multi-probe, time-domain, and multi-messenger datasets.