Node-locked phase of annual modulations from the gravitational chiral anomaly in the solar Kerr field

Abstract

The leading parity-odd mass--spin curvature invariant of the solar exterior, $P_{\odot}\equiv{}^{*}\!R\,R\simeq 288\,G^{2}M_{\odot}^{2}a_{\odot}\cos\theta/c^{4}r^{7}$, changes sign when the Earth crosses the solar equatorial plane and acts as the geometric source of the gravitational chiral anomaly. We study two minimal phenomenological responses to this structure: a long-memory reservoir $Q\propto\int(P_{\odot}-\langle P_{\odot}\rangle)\,dt$ and the local worldline derivative $D=u^{\mu}\nabla_{\mu}P_{\odot}$. Both have an annual Fourier phase fixed by ephemerides, $t^{*}=158.7$~d (June 7--8) or the opposite branch $t^{*}=341.4$~d, with a calculable secular drift of $+0.014$~d\,yr$^{-1}$ and an energy-independent geometric input phase, while predicting different semiannual fractions, $3.75\%$ and $15\%$, respectively. The response amplitudes and their microscopic origin are not predicted; the phase is. Single-amplitude fits to the digitized DAMA/LIBRA--phase2 1--3~keV residuals give $\chi^{2}/\mathrm{dof}=62.7/51$ for the reservoir and $63.6/51$ for the derivative, against $60.9/51$ for the standard-halo cosine. The most precise published phase, $t^{*}=153.5\pm3.8$~d, lies $0.3\sigma$ from the halo value and $1.4\sigma$ from the node-locked one; phase metrology at the two-day level ($\simeq3\sigma$), together with the phase-locked semiannual component, discriminates between the two clocks.