phi20_pos
plain-language theorem explainer
phi20_pos asserts that φ raised to the 20th power is strictly positive. Recognition Science astrophysicists cite it when confirming the termination shock radius scales as R_⊙ × φ^20 near 94 AU. The proof is a one-line wrapper that unfolds the definition of phi20 and applies the positivity of real powers.
Claim. $0 < φ^{20}$ where $φ$ is the Recognition Science self-similar fixed point.
background
phi20 is the definition φ^20 introduced for the termination shock radius calculation in the solar wind model. The module develops structural theorems for continuous plasma outflow driven by coronal thermal pressure gradients, with RS predictions for speeds 400-600 km/s at 1 AU and termination near 94 AU via R_⊙ × φ^20. It depends on the upstream definition phi20 := φ^20, which supplies the exact exponent for the radius scaling.
proof idea
The proof is a one-line wrapper that unfolds phi20 to expose φ^20, then applies pow_pos together with the known positivity of phi.
why it matters
This theorem supplies the positivity component inside the SolarWindCert structure, which bundles the model invariants for the solar wind outflow. It directly supports the termination shock prediction R_ts ≈ R_⊙ × φ^20 in the module, tying into the phi-ladder scaling and eight-tick octave from the forcing chain. The parent SolarWindCert incorporates it to certify overall consistency of the MHD recognition dynamics.
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