Ending the Millennium History of Deriving the "Cyclical" Law of Conservation of Energy as an Experimental Law Without Mathematical Equations Subtitle: Without the Systematic Constraint, Structural Support and Mechanistic Norm of the Interaction, Tran

The classical law of conservation of energy has long been confined to phenomenological induction and qualitative literal description, lacking fixed material basis, global operating carrier, closed‑loop evolutionary mechanism and standardized mathematical‑deduction system. As a core fundamental law of physics, for millennia it has possessed conclusions without essential underlying mechanism. Based on objective cosmic operating rules, this paper adopts the hydrogen‑helium binary system as the fundamental material basis and cosmic microwave background radiation as the dual‑function global carrier for mass‑energy balance and periodic circulation. It clarifies the essential boundary between staged mass‑energy processes and periodic steady‑state conservation, defines core conditions for critical‑circulation boundaries, and establishes a hierarchical, replicable framework‑level mathematical system. Note: this public version presents only framework equations; key analytical functions and calibrated parameters are withheld for author‑right protection and are available upon author contact for qualified‑institutional verification. This research completes theoretical closed‑loop construction from ontological existence, underlying principles, system models to framework equations, relying on three exclusive calibrated values and two‑way cross‑verification from macroscopic cosmic observations and microscopic particle‑experimental phenomena. It fills gaps in the underlying mechanism of energy conservation, revises imprecise phenomenological statements of this law in contemporary science, and deconstructs‑reconstructs part of the core system of fundamental physics, pointing toward an era of objective, mechanistically‑complete, cyclically self‑consistent basic‑physics research.