phi8_gt_46
plain-language theorem explainer
The golden ratio φ satisfies φ^8 > 46. Researchers deriving quantum coherence times from J-cost on the phi-ladder or baryon asymmetry bounds cite this inequality. The proof rewrites the power via the Fibonacci closed form and concludes via linear arithmetic with the lower bound φ > 1.61.
Claim. $φ^8 > 46$ where $φ = (1 + √5)/2$ is the golden ratio.
background
The module derives coherence times as τ_0 × φ^k at phi-ladder rungs, with τ_0 ≈ 7.3 × 10^{-15} s from the DFT-8 spectral signature. The golden ratio φ is the self-similar fixed point forced in the Recognition Science chain. Upstream results supply the identity φ^8 = 21φ + 13 (Fibonacci) and the tighter numerical bound φ > 1.61 obtained by direct comparison on the square-root definition of φ.
proof idea
The proof is a one-line wrapper that rewrites φ^8 using the Fibonacci identity φ^8 = 21φ + 13 and then applies linear arithmetic with the lower bound φ > 1.61.
why it matters
This bound is invoked inside the CoherenceTimeCert definition to certify phi-ladder amplitudes and feeds the parent result φ^16 > 2000 used in baryon asymmetry derivations. It supplies a concrete numerical anchor for the eight-tick octave (T7) and the phi-ladder mass formula in the forcing chain.
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