Objective Modern physics suffers from inherent scale fragmentation: quantum field theory holds only at the microscopic ultraviolet (UV) scale, general relativity describes the cosmic infrared (IR) scale, and Newtonian mechanics remains valid only in the intermediate macroscopic regime. No unified cross‑scale mapping rule bridges the three frameworks. Human observers are intrinsically anchored at the intermediate meter scale, and irreversible information loss occurs when probing toward either end of the scale axis, which constitutes the core bottleneck for breakthroughs in fundamental physics and engineering technology. Built upon the UV‑IR scale mirror duality hypothesis, this paper proposes a research paradigm of cross‑scale empirical laws, aiming to establish quantitative correspondence between microscopic and cosmic self‑bound systems, and to clarify the applicable boundary of each law. Methods Strong‑coupling self‑bound systems are selected as the core research samples: three‑quark bound states (protons) and quark‑gluon plasma at the microscopic end, and stellar‑mass triple‑black‑hole systems at the cosmic end. Drawing on the latest experimental observations and numerical simulation data, universal cross‑scale empirical laws are derived via dimensional matching and numerical fitting. Multi‑group orbital systems at different scales are adopted to verify the internal self‑consistency of the power law, and the applicable scope of each law is strictly defined. Results Three universal cross‑scale empirical laws are obtained by fitting: the Law of Scale Product Conservation, the Law of Frequency Product Conservation, and the revised Unified Scale‑Frequency Power Law. The duality constants for strong‑coupling systems are calibrated. The first two laws are verified to be universally valid for cross‑scale mapping. The third law is revised to serve exclusively as an internal self‑consistency constraint for orbital systems, and does not directly apply to cross‑scale numerical conversion. All orbital systems including hydrogen atomic energy levels, Solar System planets and binary star systems strictly satisfy the −3/2 power‑law index. Conclusions Microscopic and cosmic self‑bound systems follow identical dynamical structures and differ only in scale scaling. The revised three‑law system eliminates previous mismatches caused by scope overextension, forms a logically rigorous closed framework, and can be directly applied to engineering fields including noise correction for universal quantum computing and optimization of controlled nuclear fusion confinement configurations, providing empirical support for the future unification of fundamental theories.
Zheng Xinyu (Fri,) studied this question.