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

This paper derives a candidate fundamental constant—the time-dilation-force-to-rotation coupling coefficient $\gamma$—and presents the first observational constraints on its value using publicly available spin-down data from magnetars and pulsars. The constant describes the resistance exerted by spacetime structure on the rotational energy dissipation of spinning compact objects. Its theoretically derived value is $\gamma \approx 3.2 \times 10^{-20}$. Preliminary tests using published data from three magnetars yield consistent values: SGR 1806-20 gives $\gamma \approx 2.0 \times 10^{-20}$ from its observed spin-down rate during the active pre-flare period (2003–2004); Swift J1834.9-0846 gives $\gamma \approx 2.8 \times 10^{-20}$ from its braking index $n = 1.08 \pm 0.04$; and PSR J1846-0258 gives $\gamma \approx 4.2 \times 10^{-21}$ from its braking index $n = 2.65 \pm 0.01$. All three independently determined values fall within the narrow range of $10^{-20} \sim 10^{-19}$, consistent in order of magnitude with the theoretical prediction. Ordinary pulsars and millisecond magnetars yield $\gamma$ values within the same range, despite spanning four orders of magnitude in spin period and three orders of magnitude in magnetic field strength. This cross-system consistency cannot be readily explained by any existing pulsar spin-down model. We discuss the physical significance of $\gamma$ as a possible universal constant and emphasize that its universality requires further verification with a larger sample. A specific methodology and numerical prediction are provided for such future tests. (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.)