Testability: The Factor Hierarchy Law and Scientific Methodology for Multi-Factor Complex Systems—The Elevation of Factor Hierarchy Theory to the Factor Hierarchy Law and the Establishment of the Testability Norms

In any complex system driven by multiple quantifiable factors, what is the relationship among factors? Building on the empirical findings of the first six papers in this series (Tang, 2026a–2026f), this paper formally establishes the Factor Hierarchy Theory proposed by Tang (2026e) as the Factor Hierarchy Law, and for the first time proposes the Testability Principle. The law proposition—the Factor Hierarchy Law: factors naturally divide into two tiers. Regime factors determine which set of rules currently applies; their function is not reflected in direct explanatory power but in the interaction effect through which they modulate the exposure coefficients of execution factors. When a regime factor crosses a critical value, the factor weights of the entire system are systematically reset. The principle proposition—Testability: any claim about the importance of a factor in a multi-factor system must pass a complete regime-dependence test before it can be elevated from a hypothesis to reliable knowledge. Popper’s falsifiability stipulates the entry criterion for scientific knowledge, but the classic criticism of Popper’s theory within the philosophy of science has long centered on its having “only an attitudinal principle, no operational procedure”: Popper required scientists to possess a spirit of falsification, but did not specify, within multi-factor empirical research, “what counts as a rigorous test.” This paper proposes that science requires a second threshold—Testability: a procedural standard that specifies the functional dimensions that testing must cover. Falsifiability guards the entrance to science; Testability guards the exit of scientific discovery. This paper formally designates the operational implementation of the Testability Principle as the Testability Norms—comprising six functional dimensions: search completeness, modulation relationship, structural breakpoint, and causal direction as four core dimensions, together with question completeness and process closed-loop as two completeness dimensions. The Testability Norms are not bound to any specific tools—the principle is eternal, the functional dimensions are stable, and the implementation tools are replaceable. The empirical basis of the Factor Hierarchy Law comes from the systematic findings of the first six papers in this series (Tang, 2026a–2026f) across the five major market categories of finance (commodities, fixed income, currency, equity, and capital flows) and dozens of assets: the China-U.S. yield spread has been repeatedly verified as a regime factor, and when the spread crosses the zero axis, the pricing equation undergoes a structural break. The contribution of this paper lies in: formally establishing the Factor Hierarchy Theory as the Factor Hierarchy Law; establishing, after Popper’s falsifiability, a second threshold for science—Testability; and, under the Testability Principle, establishing the Testability Norms as an operational standard. It must be candidly stated that the complete empirical work of this paper is concentrated in finance. The legitimacy of elevating the Factor Hierarchy Theory to the Factor Hierarchy Law was later supported by the independent deployments of subsequent papers in the series in astronomy, statistical physics, and chemistry (Tang, 2026h–2026m, 2026s–2026u). The positioning of this paper is that of a methodological foundational paper—it establishes the Factor Hierarchy Law and the Testability Norms, and takes the systematic empirical work across the five major market categories of finance as the verification basis for the effectiveness of those norms. 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.