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This research presents the core mathematics of a universal tensional conservation theory, aiming to validate its applicability across various real-world systems.

May 1, 2026Open Access

POLIS V12: The Universal Tensional Equation — Core Mathematics, Real‑Data Validation, and Formal Counter‑Theory

Key Points

This research presents the core mathematics of a universal tensional conservation theory, aiming to validate its applicability across various real-world systems.
Introduced the universal equation and IDT metric without external parameters.
Conducted real-data validation across ten independent systems.
Included a formal counter-theory addressing objections and falsification conditions.
Confirmed all tested systems (climate, economics, physics, biology, daily life) are in Phase 4.
Demonstrated the framework's applicability to any real dataset without calibration.

Abstract

This deposit contains the core mathematics of POLIS V12, a fully closed, parameter‑free tensional conservation theory. The universal equation ε = Σ Kₘ(2+Kₘ) = 0, the IDT* metric, the iterative STOP mechanism, and the closed‑form equilibrium load Teq are presented in the main treatise. Real‑data validation across ten independent systems (climate, economics, physics, biology, daily life) confirms that all tested systems are in Phase 4. A formal counter‑theory with five objections and explicit falsification conditions is included. The framework applies to any real dataset without calibration, external parameters, or domain‑specific assumptions.

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