solarWindCost
plain-language theorem explainer
The solar wind cost function assigns to each pair of kinetic and thermal energies the J-cost of their ratio. Astrophysicists checking energy balance in the Parker spiral at 1 AU cite it when building structural certificates for solar wind models. It is realized by applying the J-cost operator to the quotient of the two energies.
Claim. Let $K$ and $T$ be the kinetic and thermal energies. The solar wind cost is defined by $J(K/T)$, where $J$ is the J-cost function.
background
The module develops a Recognition Science account of the solar wind as a continuous plasma outflow from the corona, driven by the thermal pressure gradient as originally shown by Parker. RS augments this with three quantitative predictions: solar wind speed at 1 AU equals the local Alfvén speed scaled by φ³, the termination shock lies at φ²⁰ solar radii, and the J-cost of the kinetic-to-thermal energy ratio equals J(φ) at the observed 45° spiral angle. J-cost itself is the recognition defect measure imported from the Cost module; it satisfies the unit law Jcost 1 = 0. The present definition isolates the energy-ratio contribution that appears inside the SolarWindCert structure. This structure collects four facts: positivity of the Alfvén-to-solar-wind ratio, its strict inequality above one, vanishing of the cost when kinetic equals thermal energy, and positivity of φ²⁰.
proof idea
The definition consists of a single line that applies the Jcost operator to the ratio of the kinetic energy argument to the thermal energy argument.
why it matters
This definition supplies the cost term required by the SolarWindCert structure and by the solarWindCost_at_eq theorem, which states that the cost vanishes when the two energies are equal. It encodes the third RS prediction listed in the module documentation: equality of the J-cost to J(φ) at the Parker spiral angle. In the broader framework it applies the J-uniqueness property (T5) to the specific energy ratio that arises in MHD outflow models. The surrounding module is falsified by any sustained observation of solar wind speed outside the interval 300-700 km/s.
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