Feynman Rules on the Spoke Geometry: Multi-Dimensional Propagators and the Derivation of Standard Model Couplings from D = 11

We derive the Feynman rules for quantum field theory on the extended Randall-Sundrum hub-and-spoke geometry with D = 11 dimensions, N = 7 spokes, and warp depth kL = 37. Every propagator carries three labels: a 4D spacetime position xᵐ, a spoke index s ∈ 1,. . . , 7, and a bulk coordinate c ∈ 0, 1. Electromagnetic vertices are spoke-diagonal (conserving spoke number), gravitational vertices are spoke-universal (summing over all spokes), and strong vertices are spoke-pairing (connecting distinct spoke pairs). From these rules we derive: (i) the strong coupling constant αₛ = αN²/3 from the ratio of spoke-pairing to spoke-diagonal one-loop diagrams, (ii) the reverberation damping hierarchy 1: 42: 98 from spoke-exchange loop topology, (iii) the (1+1/kL) correction to the Higgs effective potential from KK mode exchange on each hidden spoke, (iv) the dark matter fraction (N−1) /N from the graviton spoke-sum, and (v) the strong CP result θ = 0 from Z₂ spectral pairing of the boundary Dirac operator. The formalism provides rigorous derivations of results previously obtained by dimensional analysis and geometric argument, and generates new predictions for KK mode signatures at colliders.