The Factor Hierarchy System: A Unified Theoretical Framework for Cross-Disciplinary Complex Systems Research

This paper systematically expounds the “Factor Hierarchy System” as a unified conceptual framework for cross-disciplinary complex systems research. The system is built upon forty-seven preceding papers and consists of four components: the Information Isomorphism Law (epistemological foundation), which reveals that statistical structure carries information about regime structure; the Factor Hierarchy Law (ontology), which clarifies that factor functions divide into regime factors and execution factors; the Testability Principle (epistemological standard), which stipulates that claims about factor importance must undergo regime-dependence testing; and the Testability Norms (methodology), which provides standardized testing procedures across six functional dimensions. The four exhibit a four-layer progression of “epistemological foundation → ontology → epistemological standard → methodology,” with a minimal core of two laws, one principle, and one norm. The same system appears in the natural sciences, philosophy, and engineering respectively as the “Factor Hierarchy System,” “Information Isomorphism Epistemology,” and the “Scientific Discovery Operating System.” The core work of this paper includes: integrating the functional complementarity, operational connection, and axiomatic structure of the two laws; unifying the core theorem system constituted by fifteen mathematical papers and one philosophical thematic paper; consolidating the verification results across six empirical disciplines, six theoretical demotions, and three tool replacements or extensions; and delineating the philosophical orientations and applicable boundaries of the system. This paper candidly declares: all verification comes from the same author’s series of preprints and has not yet undergone independent third-party replication; the verification levels across the six disciplines differ; at least seven mathematical papers contain substantive negative results; and all 81 open problems are detailed in the three mathematical series surveys. 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.