The Construct Law of Universal Resonance: A Discrete Timing Solution to the Hubble Tension

This paper presents the formal derivation of the Construct Law, a foundational physicalprinciple proposing that universal stability is maintained through a completion-locked struc-tural anchor. We introduce the Anchor Equation, C[X] = 0, which defines a state-spacemanifold governed by a nonresonance field. By mapping this structural requirement toa modulated timing channel, we demonstrate that late-universe expansion is not a con-tinuous linear process but a harmonic evolution regulated by Fibonacci-indexed envelopes(Ln ∝ F 2n ). This framework provides a predictive, operational definition of energy as aratio of structural admissibility to modulated temporal flow. Our analysis of independenttiming-sensitive datasets, including Pantheon+ Type-Ia supernova stretch and TDCOSMOstrong-lens time delays, reveals a phase-aligned signal with a decisive Bayes Factor (prob-ability of accidental fluke ≈ 1.7 × 10−6). By accounting for this discrete timing drift, theCL-Anchor framework effectively resolves the 5σ Hubble tension, reconciling early and late-universe measurements into a single, mathematically coherent frequency without violatingthe constraints of geometry-only cosmological probes.