Momentum is all you need

The Momentum-First (M-First) framework reconstructs relativistic physics from momentumprimacy. Its core postulate of absolute directional momentum conservation uniquelydetermines an internal-external momentum coupling ($p_{k^\pm} = M(p) \pm \frac{1}{2}p_k$)and yields the emergent relativistic energy scale $M(p) = \sqrt{p_f^2+p^2}$ (with $p_f=m_0c$).Crucially, these foundational kinematics and the framework's proposed quadratic form forgravitational interactions find direct theoretical derivation within M-Theory matrix models\cite{Klaveness2025BFSS}. Gravity (Postulate 3) acts distinctly, modifying this core relation via$M_g = \sqrt{M(p)^2 + \Phi_g(g^{\mu\nu}, p_k, p_f)}$, where $\Phi_g$ exhibits a systematic,$p_f$-dependent structure \cite{Klaveness2025QFT}. Consistency with General Relativity yields a local potential$\Phi_g^{\text{local}} = p_f^2(-g_{00}-1)$, leading to a reduced effective rest energy$M_g(\text{at rest}) = p_f\sqrt{-g_{00}}$. This predicts gravitationally enhanced quantumtunneling (Gamow exponent scaled by $(-g_{00})^{1/4}$ \cite{Klaveness2025Dirac}), offering aresolution to the neutron star shallow heating puzzle with testable astrophysicalcorrelations \cite{Klaveness2025Dirac, KlavenessNSCrust}. The framework also provides an intrinsic $p_f$-dependent mechanismfor screening cosmic expansion \cite{Klaveness2025Cosmo}. This paper establishes M-First'score logic and key results; detailed derivations and further applications are in companion works.