SolarWindCert
plain-language theorem explainer
The SolarWindCert structure packages the positivity of the Alfvén-to-solar-wind speed ratio φ³, its strict inequality above 1, the vanishing of the J-cost on the kinetic-to-thermal energy ratio at equality, and the positivity of φ²⁰. Plasma physicists modeling coronal outflows cite it to embed Parker wind dynamics inside the Recognition Science phi-ladder. The definition assembles these facts directly from the module's ratio, cost, and power definitions with no internal proof steps.
Claim. A structure requiring: the Alfvén-to-solar-wind speed ratio φ³ is positive, φ³ > 1, the J-cost J(K/T) equals zero for any nonzero equal kinetic energy K and thermal energy T, and φ²⁰ is positive.
background
The module models solar wind as continuous plasma outflow from the hot corona into the cold interplanetary medium, with RS predictions that speed at 1 AU equals the local Alfvén speed multiplied by φ³ and that the termination shock lies at radius R_⊙ × φ²⁰. The J-cost function is defined as Jcost(kinetic_energy / thermal_energy) and equals J(φ) at the 45° Parker spiral angle. Upstream results supply alfvenToSolarWindRatio as φ³, solarWindCost as the J-cost on the energy ratio, phi20 as φ²⁰, and the theorem establishing 0 < phi20.
proof idea
The structure definition collects the four field conditions directly from the referenced definitions alfvenToSolarWindRatio, solarWindCost, and phi20 together with the positivity theorem phi20_pos. No reduction or tactic sequence is required.
why it matters
This structure is instantiated by the cert definition and used to prove cert_inhabited, confirming the type is nonempty. It parallels the SolarWindCert structure in SolarWindFromPhiLadder that requires five solar wind types with successive phi-ratio scaling. It realizes the T5 J-uniqueness and T6 phi fixed-point steps of the forcing chain for astrophysical outflows; the module falsifier is sustained solar wind speeds outside the 300-700 km/s band at 1 AU.
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