pith. sign in
def

G_rs

definition
show as:
module
IndisputableMonolith.Constants.GravitationalConstant
domain
Constants
line
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papers citing
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plain-language theorem explainer

G_rs gives Newton's gravitational constant in RS units as phi^5 over pi. A physicist working on constant derivations from the forcing chain cites this to eliminate free parameters in G. It arises by direct substitution of the RS scales into the ledger formula for G.

Claim. In RS-native units, Newton's gravitational constant is given by $G = phi^5 / pi$, where $phi$ is the self-similar fixed point forced by the recognition composition law.

background

Module C-002 formalizes the RS derivation of G. The general form is G = lambda_rec^2 c^3 / (pi hbar). With RS choices lambda_rec = 1, c = 1, hbar = phi^{-5}, this simplifies to phi^5 / pi. Constants.G supplies the general expression (lambda_rec^2) * (c^3) / (Real.pi * hbar). Related work in ConstantDerivations treats G as the curvature extremum, and JCostInflaton sets the J-cost to cosh t - 1. The local setting resolves the registry item on what fixes G via the T0-T8 chain.

proof idea

Direct definition via substitution of RS unit choices into the general G from Constants.

why it matters

Used by gravitational_constant_derived to close C-002 and by all_constants_from_phi to list constants from phi. It supplies the framework value G = phi^5 / pi. Supports the eight-tick octave and D = 3 but leaves open exact CODATA agreement.

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