alfvenToSolarWindRatio_pos
plain-language theorem explainer
The theorem establishes that the Alfvén-to-solar-wind speed ratio is strictly positive. Researchers modeling solar wind outflows within Recognition Science cite it to confirm the scaling factor φ³ remains positive before constructing velocity predictions. The proof is a one-line wrapper that unfolds the definition and applies the positivity of real powers.
Claim. $0 < φ^3$ where $φ$ is the golden ratio.
background
In the Solar Wind from MHD Recognition Dynamics module the solar wind speed at 1 AU is given by v_sw = v_A × φ³ with v_A the Alfvén speed at the corona base. The constant φ arises as the self-similar fixed point forced in the T0–T8 chain. The upstream definition alfvenToSolarWindRatio sets the ratio explicitly to φ³, and the module imports Constants to supply phi_pos.
proof idea
The proof is a one-line wrapper. It unfolds alfvenToSolarWindRatio to φ³ and applies pow_pos to the already-established positivity of φ.
why it matters
This theorem supplies the alfven_ratio_pos field required by the SolarWindCert structure in cert. It closes the positivity requirement for the RS solar wind model that uses the eight-tick octave and D = 3, consistent with the Parker spiral and termination-shock predictions stated in the module doc-comment. No open scaffolding remains for this specific claim.
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