Technical Specification for the Scientific Discovery Operating System: Mathematical Formalization and Engineering Architecture —A Proceduralized Knowledge Discovery Protocol Based on the Factor Hierarchy Law and Testability Norms

Abstract

Tang (2026g) established the theoretical framework of the Scientific Discovery Operating System, providing the first complete definition of the Factor Hierarchy Law—including the dichotomy of regime factors and execution factors, the three morphologies of regime factors (pure regime factors, dual-identity factors, and pure execution factors), the Testability Principle, the six functional dimensions of the Testability Norms and their core commitment that "functional dimensions are eternal, implementation tools are replaceable," and first establishing testability as the second gateway after Popperian falsifiability, i.e., the third foundation of scientific methodology (following Bacon's experimental method and Popper's falsifiability). Tang (2026r) subsequently positioned the Factor Hierarchy Law as "the law of meta-laws," unified the three components into the Scientific Discovery Operating System, and first proposed the openness of the operating system—that not only the tool layer is replaceable, but the number of functional dimensions themselves may be expanded or streamlined in the future—thereby establishing the fourth foundation of scientific methodology. This paper completes the mathematical formalization and engineering architecture design of the operating system on the basis of the above theoretical foundations, establishing it as a complete technical specification. This paper does not redefine or prove the mathematical kernel of the operating system—the kernel is constituted by the axioms and theorems in Tang (2026g) and Tang (2026r). What this paper defines are the calling interfaces of the kernel, the data flow protocols among modules, and the architectural constraints for engineering implementation. The core contributions include: (1) complete mathematical formalization of the MRSD algorithm (Multi-Regime State Decoupling Algorithm)—the core engine of the operating system responsible for automatically detecting the positions, quantities, and types of regime-switching breakpoints from objective data, including the acceptability conditions for the input data matrix, the mathematical definition of the structural optimization operator with its equivalence declaration to the Bai-Perron algorithm, and the formalized structure of the output regime division matrix; (2) engineering architecture of the audit engine—strict separation of functional requirements (irreplaceable architectural norms) from currently recommended tools (replaceable algorithmic implementations) across four core inspection modules (Search Completeness, Modulation Relation, Structural Breakpoint, Causal Direction), with functional requirements explicitly designated as irreplaceable architectural norms and specific tools designated as currently recommended implementations, and the cross-validation rule of the Structural Breakpoint module precisely defined as multi-category independent tool verification, including behavioral semantics for tie-breaking arbitration and rule weights for activation operator stratification; (3) the Tool-Layer Replaceability Principle—tools may be replaced under the condition of satisfying functional requirement constraints, with equivalence verification on standard datasets required before replacement, and tool divergence itself identifying regions requiring further investigation; (4) formalized declaration of the operating system as an open protocol—output reliability depends solely on the objectivity of the input data and the transparency of the algorithmic structure; (5) complete mapping between engineering modules and cross-disciplinary verification—demonstrating the precise correspondence between each engineering module and the twenty-five empirical papers; (6) comprehensive tool-layer summary—systematically organizing all tools actually used across the twenty-five papers, classified by the six functional dimensions; (7) prospective outlook—based on the verified theoretical foundations, envisioning the potential impacts of full deployment of the operating system and clarifying the verification pathway from blueprint to reality. Upon completion of these tasks, any competent software engineer may independently implement an operating system normatively equivalent to that described in this paper, relying only on this paper, Tang (2026g), and Tang (2026r). The reliability of this system is jointly guaranteed by rigorous mathematical structure, statistical foundations, and cross-disciplinary empirical verification. 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.