phi_pos
plain-language theorem explainer
The golden ratio φ satisfies φ > 0. Researchers deriving the golden ratio from J-cost minimization in the Recognition Science framework cite this as the basic positivity property needed for the φ-ladder. The proof is a one-line term wrapper that invokes the corresponding fact inside the Constants structure.
Claim. Let φ denote the golden ratio. Then φ > 0.
background
The Φ-Emergence module derives the golden ratio from J-cost minimization. The Constants structure from LawOfExistence bundles CPM constants including φ, with nonnegativity constraints such as 0 ≤ Knet. Upstream results supply the abstract bundle definition and collision-free program classes that underwrite the constant extraction.
proof idea
This is a one-line wrapper that directly applies Constants.phi_pos from the LawOfExistence module.
why it matters
The result supplies the positivity foundation for the φ-ladder and self-similarity properties in the Recognition framework, directly supporting T5 J-uniqueness and T6 phi fixed-point emergence. It fills the initial positivity step in the φ-Emergence module whose doc-comment states the derivation from J-cost minimization. No open questions are addressed.
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