kappa_einstein
plain-language theorem explainer
The definition supplies the Einstein gravitational coupling κ = 8πG/c⁴ in RS-native units with c = 1. Researchers matching discrete Regge curvature to the continuum Einstein-Hilbert action cite this constant when scaling the stress-energy term. It arises by direct substitution of the RS-derived G = λ_rec²/(π ℏ) with ℏ = φ^{-5}.
Claim. The Einstein coupling constant is defined by $κ = 8π G / c^4$, where $G$ is the RS-native gravitational constant $G = λ_{rec}^2 c^3 / (π ℏ)$ with $ℏ = φ^{-5}$ and $c = 1$.
background
Recognition Science derives G from the J-cost functional J(x) = (x + x^{-1})/2 - 1 together with the forcing chain that fixes φ as the self-similar point and sets ℏ = φ^{-5}. The module collects all such constants in units where the fundamental tick τ₀ = 1. The upstream definition of G supplies the explicit algebraic form λ_rec² c³ / (π ℏ) that is inserted here.
proof idea
The declaration is a direct one-line definition that substitutes the RS expression for G into the classical Einstein coupling formula. No lemmas are applied inside the definition itself.
why it matters
kappa_einstein supplies the scaling factor in the field-curvature identity of ContinuumTheorem.field_curvature_identity_einstein and in bridge_chain_complete, where the discrete Regge sum is equated to the continuum Einstein term. It is the coefficient in front of T_μν and appears in the GDerivationChain that links Q3 geometry through J-uniqueness (T5) to the eight-tick octave. The downstream lemma kappa_einstein_eq reduces it to 8φ^5.
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