Modified Dirac Dynamics in Curved Spacetime from Momentum-First Principles

Solutions to the Dirac equation are constrained using the Momentum-First (M-First)framework, where gravity modifies the full energy-momentum relation via$M_g^2 = M_{\mathrm{flat}}^2 + \Phi_g$, with$\Phi_g \equiv (H_{GR}/c)^2 - M_{\mathrm{flat}}^2$. This paper explores theconsequences for Dirac fermions (rest mass $m_0$, intrinsic fermic momentum $p_f=m_0c$),including: (i) how $\Phi_g$ (a function of metric $g^{\mu\nu}$, canonical momenta $P_k$,and $p_f$) impacts both contextual fermic and kinetic contributions to thegravitationally influenced core momentum $M_g$; (ii) the derivation of gravitationallymodified quantum directional momentum operators for static fields,$\hat{\mathcal{P}}_{k^\pm}^{(g)} = N(\hat{x})\hat{M}_{\text{flat}}(\hat{P}) \pm\frac{1}{2N(\hat{x})}\hat{P}_k$, revealing changes to the particle's internalmomentum structure and leading to modified uncertainty relations (where $N(\hat{x})=\sqrt{-g_{00}(\hat{x})}$); (iii)phenomenological predictions such as enhanced pycnonuclear tunneling in neutron stars(from the gravitationally influenced rest core momentum $M_g(\text{rest})=N(\vec{r})p_f$, implying a contextual rest mass $m_0^{\text{contextual}}=N(\vec{r})m_0$) andpotentially flavor-dependent neutrino dynamics. Cosmological effects from the distinctcosmic drift modifier $\phi_{\mathrm{drift}}$ are also briefly considered.