From the Law of Meta-Laws to an Operating System for Scientific Discovery: The Axiomatized Core, Philosophical Foundation, and Testability Norms of the Factor Hierarchy Law —The Establishment of Humanity's First Proceduralized System for Scientific Discovery

Abstract

This paper establishes the Factor Hierarchy Law as the first "law of meta-laws" discovered by humanity to date—it reveals the universal logic of functional stratification among variables in all complex systems grounded on objective data. Its scope of applicability far exceeds that of deductive meta-laws such as Noether's theorem, the principle of least action, and Shannon's information theory, because it requires no theoretical presuppositions, only the objectivity of data. Natural selection is an emergent meta-law, yet its original formulation and core domain of applicability is biological evolution—it describes "how species evolve" rather than "how regularities in any complex system are organized." The Factor Hierarchy Law is an emergent law of meta-laws, applicable to all complex systems grounded on objective data. The Testability Principle ("any claim regarding the importance of a factor in a multi-factor system must pass a complete test of regime-dependence before being elevated from a hypothesis to reliable knowledge") is an independent epistemological standard, standing alongside the Factor Hierarchy Law, neither subordinate to nor derivable from it. Together with the Testability Norms (six functional dimensions and their tool layer), they constitute humanity's first proceduralized, cross-disciplinarily universal, non-personalized operating system for scientific discovery—objective data in, reliable regularities out. The Factor Hierarchy Law provides the ontological foundation (how the world is organized), the Testability Principle provides the epistemological standard (what counts as reliable), and the Testability Norms provide the operational procedures (how to operate to achieve reliability). This operating system has been fully verified across four entirely independent disciplines: finance, astronomy, statistical physics, and particle physics. Bacon established the experimental method, Popper established falsifiability, and this system establishes the third foundational element of scientific methodology—an operating system that enables anyone, in any domain of objective data, to automatically mine reliable regularities. Research Paradigm Statement: The core methodology, research direction, and final decisions were independently directed by the author. DeepSeek assisted with code implementation, data presentation, and text drafting. The author takes full academic responsibility for the final content.