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August 20, 2026Open Access

Testability: The Factor Hierarchy Law and Scientific Methodology for Multi-Factor Complex Systems—Complete Empirical Evidence from Global Asset Pricing, Multi-Dimensional Astronomical Verification, and First-Principles Calibration in Physics

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STShuiping Tang

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Overview

Cross-disciplinary empirical analysis reveals hierarchical rule factors and structural breakpoints across financial, astronomical, and physical systems, establishing operational testability norms.

Key Points

  • Formulate the Factor Hierarchy Law and define operational Testability Norms to evaluate how master rule factors govern multi-factor complex systems across distinct regimes.
  • Evaluated empirical datasets across global finance (China–U.S. interest rate spread across five major markets), astronomy (stellar atmospheric models and transit depth), and theoretical physics (2D Ising model).
  • Established Testability Norms spanning six functional dimensions: search completeness, modulation relationship, structural breakpoint, causal direction, question completeness, and process closed-loop.
  • Verified the China–U.S. interest rate spread as a rule factor in finance that triggers structural breaks in asset pricing equations when crossing the zero axis.
  • Identified structural breaks across five independent astronomical dimensions at the stellar transition boundary (4400–5800 K, critical point 4762 K, log g = 4.64).
  • Demonstrated exact information-theoretic duality with Ehrenfest phase transitions and zero detection bias calibrated against Onsager's exact solution for the 2D Ising model.

Cite This Study

Shuiping Tang (2026) studied this question.

synapsesocial.com/papers/6a86b5978a91293e6a1cd010https://doi.org/10.5281/zenodo.21988326
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