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 \[2A_{}Gμν⁽¹⁾=Tμνᵖʰʸˢ,_u={1}{16π A_{}}=0.0497534… .\] 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, \[G=C_u{c^5t_0\,2}{{a}_{}}=Cφ{c^5τ_G\,2}{{a}_{}},τ_G=τ̄\,t_0,φ={C_u}{τ̄\,2}.\] 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 \(rCs/e=ωCs/ω_e\). The atomic factor-through theorem places every remaining absolute component of this atomic-to-SI map on one electron–gravity frequency ratio: \[χeG=ω_e/Ω_G>0,_G(Cs)=rCs/eχeG,N,atomic[SI]=KeGχeG\,2.\] Here \(KeG\) is the specified forward coefficient; \(χeG\) remains uncomputed. The atomic route is therefore a one-scalar family, not an independent numerical SI prediction. The declared canonical local chart closes at \(6.67430×10⁻¹¹\,{m^3\,kg⁻¹\,s⁻²}\), whereas the specified Friedmann input set gives \(6.72048×10⁻¹¹\,{m^3\,kg⁻¹\,s⁻²}\) 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.