The Information Isomorphism Law: A Meta-Law Spanning Ontology and Epistemology ——Tracing the Necessary Premise from the Cross-Disciplinary Success of the Scientific Discovery Operating System

Abstract

The Scientific Discovery Operating System (Tang, 2026g, 2026r) has been successfully deployed across six completely independent disciplines, yet a fundamental question has never been systematically addressed: Why is this operating system effective? This paper's answer is: because in complex systems grounded in objective data and exhibiting regime switching, statistical structures carry the information of regime structures. This ontological fact is formally named herein as the Information Isomorphism Law. The argumentative path of this paper is not induction from specific discoveries to a universal principle, but a retracing from the operating system's success to its necessary premise: the six functional dimensions of the Testability Norms—Search Completeness, Modulation Relationship, Structural Breakpoints, Causal Direction, Problem Completeness, and Process Closure—together constitute a multi-dimensional probe of statistical structures. If statistical structures contained no information traces of regime switching, this methodology could not have succeeded repeatedly across six disciplines. Therefore, the success of the operating system itself proves the establishment of the Information Isomorphism Law. The Chow F-order parameter duality (Tang, 2026k) and the intercept/slope ratio-critical distance duality (Tang, 2026x, Theorem A) provide precision verification for this law on a truth-known system, rather than serving as its inductive basis. The Information Isomorphism Law is an ontological law—it asserts a fundamental fact about how the world is organized: "Statistical structures carry the information of regime structures." Precisely because it describes the special fact of "information carrying," it is naturally and simultaneously an epistemological meta-law—it answers the fundamental question of "how we can know the world." The Factor Hierarchy Law (likewise a meta-law) simultaneously revealed, at the moment of its discovery, both an organizational principle of the world and the statistical visibility of that principle—it inherently carries an epistemological dimension. The Information Isomorphism Law is the universalized extraction of this original unity—it separates "visibility" from the specific content of the Factor Hierarchy Law and establishes it as a universal law applicable to all regime switching across all statistical dimensions. The two laws are complementary, jointly constituting the complete philosophical foundation of the Scientific Discovery Operating System. Within the operating system, the Information Isomorphism Law occupies the epistemological foundation layer, completing a comprehensive four-layer structure. It must be candidly acknowledged that the Information Isomorphism Law was explicitly proposed only after the completion of the preceding 28 papers—historically, the operating system was successfully deployed first, and only later understood as to why it is effective. The contribution of this paper lies not in "inventing" information isomorphism, but in explicitly naming and systematically demonstrating this law for the first time, thereby completing the epistemological closure of the operating system. 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.