G_rs_eq
plain-language theorem explainer
The RS-native gravitational constant equals φ^5 with φ the golden ratio. Researchers deriving constants from the Recognition Science foundation cite this when fixing the mass scale at 1/φ^5. Reflexivity on the explicit definition of G_rs as φ_val to the fifth power completes the proof.
Claim. In Recognition Science native units the gravitational constant satisfies $G_{rs} = φ^5$, where $φ$ denotes the golden ratio.
background
The Constant Derivations module shows how c, ħ, G and α arise as ratios from the RS foundation rather than free parameters. The chain runs from the Composition Law through J-uniqueness to φ as self-similar fixed point, D = 3, the eight-tick period τ₀ = 8, and finally G as curvature extremum with natural mass scale M₀ = 1/φ^5. G_rs is introduced as the RS-native gravitational constant expressed via this scale.
proof idea
The proof is a term-mode reflexivity that matches the definition of G_rs directly to φ_val raised to the fifth integer power.
why it matters
This equality anchors the gravitational constant at Level 4 of the derivation chain in the module doc-comment. It isolates the φ^5 factor that appears in the upstream G expression λ_rec² c³ / (π ħ) once c = 1 and ħ = φ^{-5} are substituted, and it supports downstream use in Gravity.JCostInflaton and Papers.GCIC.BekensteinFromLedger.
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