r_ref_phi_rung_approx
plain-language theorem explainer
The definition assigns 364 as the approximate phi-rung for the reference scale r_ref in the 20 nm / 32x gravitational running prediction. Researchers modeling nanoscale strengthening of G cite this rung to locate the correction scale on the phi-ladder. The assignment is a direct constant definition accompanied by a note on proximity to the 360-unit RS sync period.
Claim. The approximate rung on the $phi$-ladder for the reference radius $r_{rm ref}$ in the 20 nm / 32$times$ gravitational enhancement prediction equals 364.
background
The module formalizes running of Newton's constant at nanometer scales, with $G_{rm eff}(r)$ approaching $G_infty$ at large $r$ and reaching approximately 32 times $G_infty$ at $r$ near 20 nm. The running exponent $beta$ equals $-(phi-1)/phi^5$. The reference scale $r_{rm ref}$ sits at a rung on the phi-ladder, where lengths are given by period$(k) := phi^k$ from the pulsar emission module. Upstream structures include collision-free classes and simplicial edge lengths that support the underlying ledger.
proof idea
The declaration is a direct definition that assigns the natural number 364, with the inline comment observing closeness to the RS sync period of 360.
why it matters
This rung value feeds the RunningGR4Cert structure that certifies the full set of running G predictions, including the explicit $r_{rm ref}$ inequalities and the hypothesis H_GravitationalRunning. It connects to the eight-tick octave (T7) by lying 4 units from the lcm(8,45) = 360 period. The downstream theorem rung_near_sync_period establishes the exact offset using this definition.
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