G_rs
plain-language theorem explainer
The declaration supplies the RS-native gravitational constant as the fifth power of the golden ratio. Workers deriving constants from the forcing chain cite it to show G arises directly from ledger curvature without external parameters. The definition is a direct assignment of phi_val to the fifth integer power.
Claim. In Recognition Science native units the gravitational constant satisfies $G = phi^5$, where $phi$ denotes the golden-ratio fixed point of the J-cost.
background
The module derives the physical constants from the RS foundation via the Composition Law, the unique J-cost $J(x) = (x + x^{-1})/2 - 1$, the self-similar fixed point phi, the eight-tick period, and D = 3. G is obtained as the curvature extremum once the fundamental length and time scales are fixed by the ledger geometry. The supplied DOC_COMMENT states that in RS-native units with mass scale $M_0 = 1/phi^5$ one obtains $G = phi^5$. Upstream results include the general expression $G = lambda_rec^2 c^3 / (pi hbar)$ and the CODATA value, both reduced to the same algebraic form once $c = 1$ and $hbar = phi^{-5}$ are substituted.
proof idea
One-line definition that directly assigns the value phi_val raised to the fifth integer power.
why it matters
It supplies the pure phi^5 term required by gravitational_constant_derived (which resolves C-002) and by all_constants_from_phi. The parent theorem gravitational_constant_derived combines this definition with the pi factor arising from the holographic bound. The result sits at Level 4 of the derivation chain in the module document and closes the T6-to-T8 segment of the forcing chain by fixing the curvature scale algebraically in phi.
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