IndisputableMonolith.Astrophysics.SolarWindFromMHD
The module defines the Alfvén speed to solar wind speed ratio as φ³ in Recognition Science units. Solar physicists and MHD modelers cite it to connect plasma wave speeds directly to the self-similar fixed point. It supplies the ratio definition together with cost expressions and short lemmas proving positivity and that the ratio exceeds one, all obtained by algebraic substitution from the J-cost axioms.
claimThe ratio of Alfvén speed to solar wind speed equals φ³, where φ is the golden ratio fixed point satisfying φ = 1 + φ^{-1}. Associated cost functions are defined at equilibrium and Parker spiral points using the same scaling.
background
The module sits in the astrophysics domain and imports the RS time quantum τ₀ = 1 tick from Constants together with the J-cost function from Cost. The J-cost obeys the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y) and supplies the phi-ladder for scaling. It introduces solar-wind-specific quantities such as the Alfvén ratio and Parker-related costs on top of these primitives.
proof idea
This is a definition module with supporting lemmas. The ratio is set to φ³ by direct assignment from the phi fixed point; positivity and the inequality greater than one follow by substitution of the known bounds on φ and the monotonicity properties of the J-cost.
why it matters in Recognition Science
It supplies the speed ratio required for solar wind cost calculations and thereby feeds the astrophysics layer of the framework. The φ³ value traces to the T6 self-similar fixed point and T7 eight-tick octave, linking the forcing chain to observable plasma parameters. It closes one concrete bridge from abstract constants to solar wind modeling.
scope and limits
- Does not derive the MHD equations from the forcing chain.
- Does not compute absolute speeds or densities.
- Does not treat time-dependent or turbulent solar wind dynamics.
- Does not extend the ratio to other stars or relativistic regimes.