What question did this study set out to answer?

To challenge the static paradigm of physics by proving that fundamental constants are dynamic rather than fixed.

July 20, 2026Open Access

PFUSRC-097 The Unified Origin of the ₁ Dynamic Rhythm Constant and the Dynamic Planck Constant—The Collapse of the Static Physics Paradigm and the Topological Closure of a Dynamic Cosmos

Key Points

To challenge the static paradigm of physics by proving that fundamental constants are dynamic rather than fixed.
Proposed a triple coaxial biconical topological system with an 11-dimensional framework.
Developed a unified expansion formula for four-dimensional flow variables.
Derived and proved a locally dynamic variation of the Planck constant influenced by topological and flow variables.
Demonstrated that classical π is a low-curvature steady-state approximation, while π_{1} represents a dynamic rhythm.
Established h_{eff} as a locally dynamic quantity influenced by spacetime curvature and flow variables.
Outlined a closed-loop system that connects topology, flow-variable rheology, and cosmic rhythm, affirming the dynamic nature of physical constants.

Abstract

The foundational framework of classical and modern quantum physics rests on the core assumption that fundamental physical constants are globally static and invariant. The static π and the static Planck constant h are regarded as the fixed underlying yardsticks of the cosmos, forming the bedrock of the three-hundred-year-old static universe paradigm. This paradigm directly prevents the self-consistent unification of quantum mechanics and general relativity, producing a series of irremediable theoretical flaws: singularity divergences, renormalization difficulties in quantum field theory, deviations in early-universe spectral lines, and the muon g-2 anomaly. These are the core logical fractures of the mainstream physical system. Based on the PFUSRC 11-dimensional triple coaxial biconical topological system, the unified expansion formula of four-dimensional flow variables, and the biconical convergence-expansion steady-state theorem, this paper accomplishes two core paradigm restructurings. First, it strictly distinguishes the three-layer structure of π: pure mathematical abstract π, 3D physical static slice π, and 11D topological dynamic ₁, proving that classical π is merely a frozen special case of low-curvature steady-state spacetime, while ₁ is the true dynamic rhythm base governing interlayer phase evolution and biconical topological deformation. Second, it derives and proves that the Planck constant is not a global absolute constant, but a locally dynamic derived quantity — h₄₅₅ — jointly determined by the ₁ topological rhythm, spacetime curvature, and the latching density of four-dimensional flow variables. This paper simultaneously establishes the cosmic time-evolution law of ₁, the coupled mechanism of the dynamic uncertainty principle, and the local steady-state shielding mechanism, completing the fourfold homogeneous unification of biconical topology, flow-variable rheology, the ₁ cosmic rhythm, and the h₄₅₅ quantum scale. It shatters the final barrier of static physics, terminates the static-constant-dominated cosmic cognitive paradigm, and establishes a fully self-consistent closed-loop system of a dynamic topological cosmos, providing complete ontological and mathematical support for unifying quantum effects, spacetime gravity, cosmic evolution, and microscopic anomalies.

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