kappa_derived

In the gravitational sector the lattice field encodes the metric perturbation $h_{\mu\nu}$ in harmonic gauge. Stationarity of the J-cost action linearizes to a lattice Laplacian; in the continuum limit that becomes $\nabla^2 h = 0$ (vacuum) or $\nabla^2 h = -2\kappa T$ (sourced). The module replaces the general Cheeger–Müller–Schrader axiom by a direct cubic-lattice argument on $\mathbb{Z}^D$ with known cost $J(e^{\varepsilon})=\cosh\varepsilon-1$.

The coupling $\kappa$ is not fitted. Upstream, the zero-parameter gravity layer defines $\kappa_{\mathrm{RS}}:=8\phi^5$ and records the closed form $\kappa_{\mathrm{RS}}=8\phi^5$ by reflexivity. Here $\phi$ is the golden ratio forced as the self-similar fixed point (forcing chain T6), and the factor $8\phi^5$ is the RS-native Einstein constant in units where $c=1$.

One-line wrapper: apply the upstream closed-form theorem stating $\kappa_{\mathrm{RS}}=8\phi^5$. That theorem is definitional reflexivity on the noncomputable definition $\kappa_{\mathrm{RS}}:=8\phi^5$. No further algebra is required.

Pins the sourced linearized EFE coefficient $\nabla^2 h=-2\kappa T$ with $\kappa=8\phi^5$, so gravity carries zero free parameters. Downstream, the continuum-bridge certificate requires a field kappa_derived asserting the J-cost-to-Regge factor equals $8\phi^5$, and records that J-cost stationarity on the simplicial ledger yields the Einstein equations with that coupling. The cubic Regge convergence certificate and the full GR certificate (and its v2) likewise consume the identity for dimension, positivity, and conservation packaging. Framework landmarks: T6 ($\phi$ forced) and the RS constants $G=\phi^5/\pi$, $\hbar=\phi^{-5}$ sit in the same $\phi$-power bookkeeping that produces $\kappa=8\phi^5$.