A Possible Universal Constant in Compact Star Spin-Down: First Observational Constraints from Magnetars and Pulsars

Starting from the theory of the pseudo time-dilation force, this paper derives a candidate fundamental constant—the time-dilation-force-to-rotation coupling coefficient $\gamma$. This constant quantifies the resistance exerted by the structure of spacetime on the rotational energy dissipation of spinning astrophysical bodies, with a theoretically derived value of $\gamma \approx 3.2 \times 10^{-20}$. A preliminary test of this constant is performed using published data from three magnetars: SGR 1806-20 yields $\gamma \approx 2.0 \times 10^{-20}$; Swift J1834.9-0846, after subtracting known wind contributions, yields $\gamma \in [2.1, 7.7] \times 10^{-21}$, with a mid-value of approximately $4.9 \times 10^{-21}$; and PSR J1846-0258 yields an order-of-magnitude estimate of $\gamma \sim 10^{-20}$. All three magnetars give $\gamma$ values falling within the narrow range of $10^{-21} \sim 10^{-20}$, consistent in order of magnitude with the theoretical prediction. This paper further demonstrates cross-system consistency using ordinary pulsars and millisecond magnetars, and discusses the physical significance of $\gamma$ as a potential universal constant. If confirmed as constant by data from a larger sample of pulsars, it would represent a paradigm shift in our understanding of spacetime—from a passive background to an active entity—and fill the gap of a fundamentally new type of interaction describing spacetime-rotation coupling. Explicit falsification conditions are provided, along with a concrete plan for future systematic verification. (Note on AI-Assisted Computation Certain mathematical derivations and physical calculations in this paper were performed by an AI tool (large language model) based on the theoretical framework and postulate system provided by the author. Specifically, the AI tool contributed to: formula derivation, equation solving, integral evaluation, series summation, and recalculation verification of established quantum mechanical results. All physical insights, core assumptions, logical premises, and the theoretical framework itself were independently developed by the author. The AI tool served solely as an auxiliary instrument for mathematical derivation and computational verification, comparable in role to symbolic computation software or numerical tools routinely employed by researchers. The author has reviewed every derived result for physical plausibility, consistency with known experimental data, and logical coherence, and assumes full responsibility for all conclusions. This statement is provided in the interest of academic transparency, while clearly distinguishing between the originality of ideas and the auxiliary role of computation.)