A First-Principles Derivation of Newton's Gravitational Constant from an Eleven-Dimensional Covariant Master Action

Newton's gravitational constant relates conserved stress to spacetime curvature, but its magnitude is not selected by classical general relativity. We derive the native gravitational response on a regular branch of an eleven-dimensional covariant master action. On the information–projection domain, the seven action terms are combined before their shared auxiliary variables are eliminated. The reduced spin-2 response is then normalized by a conserved unit stress source. The result is \[2A_{\star}G_{\mu\nu}^{(1)}=T_{\mu\nu}^{\mathrm{phys}},\qquadC_u=\frac{1}{16\pi A_{\star}}=0.0497534\ldots .\] No observed Newton constant, measured particle mass, or reference-clock frequency selects this native coefficient. The normalized response is preserved through the four-dimensional readout hierarchy. The electron, muon, tau, up and down quarks, proton, and neutron return the same tensor coefficient at linear Einstein/stress order on the stated branch; additional scalar forces remain distinct observables. With the physical-time and action sections, the native response defines one dimensional Newton quantity, \[\boldsymbol{G}=C_u\frac{c^5\boldsymbol{t}_0^{\,2}}{\boldsymbol{\mathfrak{a}}_{\star}}=C_{\phi}\frac{c^5\boldsymbol{\tau}_G^{\,2}}{\boldsymbol{\mathfrak{a}}_{\star}},\qquad\boldsymbol{\tau}_G=\bar{\tau}\,\boldsymbol{t}_0,\qquadC_{\phi}=\frac{C_u}{\bar{\tau}^{\,2}}.\] Its weak-field restriction gives the Newton–Einstein response. On the declared leading atomic-current branch, a sixteen-dimensional caesium hyperfine operator fixes the dimensionless ratio \(r_{\mathrm{Cs}/e}=\omega_{\mathrm{Cs}}/\omega_e\). The atomic factor-through theorem places every remaining absolute component of this atomic-to-SI map on one electron–gravity frequency ratio: \[\chi_{eG}=\frac{\omega_e}{\Omega_G}>0,\qquadB_G^{(\mathrm{Cs})}=r_{\mathrm{Cs}/e}\chi_{eG},\qquadG_{N,\mathrm{atomic}}^{[\mathrm{SI}]}=K_{eG}\chi_{eG}^{\,2}.\] Here \(K_{eG}\) is the specified forward coefficient; \(\chi_{eG}\) remains uncomputed. The atomic route is therefore a one-scalar family, not an independent numerical SI prediction. The declared canonical local chart closes at \(6.67430\times10^{-11}\,\mathrm{m^3\,kg^{-1}\,s^{-2}}\), whereas the specified Friedmann input set gives \(6.72048\times10^{-11}\,\mathrm{m^3\,kg^{-1}\,s^{-2}}\) as a branch-conditioned cosmological consistency test. These are not averaged. An admissible bound-system selector removes the leading Friedmann update, while residual exchange must satisfy the same covariant conservation law. Newton's coupling is thus the dimensional realization of a conserved-stress-normalized geometric inverse stiffness.