kappa_rs
plain-language theorem explainer
kappa_rs supplies the RS value for the Einstein gravitational coupling as eight times phi to the fifth power. Workers deriving continuum gravity from the J-cost ledger lattice cite this definition when passing from discrete defect curvature to the Einstein equations. The definition is a direct algebraic assignment with no further reduction steps.
Claim. The Recognition Science gravitational coupling is defined by $κ = 8φ^5$, where $φ$ is the golden-ratio fixed point of the Recognition Composition Law.
background
The Zero-Parameter Gravity module treats gravity as large-scale curvature of the ledger lattice induced by defect distributions, not as a fundamental interaction. G-002 states that the Einstein field equations arise in the continuum limit with the specific coupling $κ = 8φ^5$. Upstream, phi is the self-similar fixed point forced by the UnifiedForcingChain (T6) and satisfies the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$. The eight-tick octave (T7) supplies the discrete factor of 8 that appears in the definition.
proof idea
Direct definition that unfolds immediately to the expression 8 * phi ^ 5. No lemmas or tactics are invoked; the value is assigned by the algebraic form required by the eight-tick structure.
why it matters
kappa_rs fixes the Einstein coupling that appears in ricci_from_source (where $R = -κ ρ$) and in the gravity_from_ledger bundle. It realizes the module claim that the Einstein gravitational constant is derived rather than postulated, closing G-002. The factor 8 originates in the eight-tick octave (T7) while $φ^5$ traces to the phi-ladder mass formula and Berry creation threshold. The definition is used by kappa_bounds to obtain the numerical interval 85.6 < κ < 90.4.
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