phi_ratio
plain-language theorem explainer
phi_ratio supplies the inverse golden ratio 1/φ as a real number drawn from the CPM constants bundle. Quasicrystal energy modelers and phi-ladder certifiers in acoustics and astrophysics cite it when establishing successive ratio equalities. The declaration is introduced by a direct one-line abbreviation of the reciprocal of the phi constant.
Claim. Let $φ$ denote the golden ratio from the CPM constants bundle. Define $φ_{ratio} := 1/φ$.
background
The Chemistry.Quasicrystal module develops quasicrystal φ-stability under Recognition Science. It states that aperiodic tilings exhibit long-range order without translational symmetry, with the golden ratio appearing in Penrose tile area ratios and icosahedral 5-fold axes. Stability follows because the energy proxy E(r) = (r - 1/φ)² reaches its minimum at r = 1/φ, the unique self-similar ratio; any deviation raises structural strain.
proof idea
The definition is a one-line wrapper that applies the phi field of the Constants structure imported from LawOfExistence.
why it matters
This definition supplies the concrete value inserted into phi_ratio fields of certification structures such as RoomAcousticsCert (requiring ∀ k, rt60(k+1)/rt60 k = phi) and the analogous CoronalTimescaleCert and GalacticRotationCert. It implements the module prediction that stable quasicrystals have tile ratios involving φ, linking to the self-similar fixed point (T6) and phi-ladder constructions in the forcing chain.
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