kappa_rs_closed_form
plain-language theorem explainer
The theorem states that the RS Einstein gravitational coupling equals exactly 8 phi to the fifth power. Researchers deriving general relativity from ledger curvature would cite this to fix the constant without free parameters. The proof applies reflexivity directly to the definition of kappa_rs.
Claim. The RS Einstein gravitational coupling satisfies $k = 8 phi^5$.
background
The Zero-Parameter Gravity module derives gravity as curvature of the ledger lattice induced by defect distributions. kappa_rs is defined as the RS prediction for the Einstein coupling, given explicitly by 8 times phi to the fifth. This follows from the J-cost framework and the forcing chain that sets phi as the self-similar fixed point.
proof idea
The proof is a one-line reflexivity that matches the theorem statement directly to the definition of kappa_rs.
why it matters
This equality supplies the explicit factor used by ricci_source_proportional_to_kappa to relate the Ricci scalar to mass density with the sign for attractive gravity. It realizes G-002 from the module documentation, confirming the Einstein equations emerge with kappa equal to 8 phi^5. The result aligns with the Recognition Science constants where G equals phi^5 over pi in native units.
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