Entropy Loss in Collatz Dynamics Linked to log2(3) — E8 Intelligence Research

FINDING: Collatz dynamics exhibit logarithmic information loss tied to log2(3), linking entropy models to the conjecture's structure. | MATH: Collatz map T(n) = n/2 if even, (3n+1)/2 if odd; average multiplicative growth per step ≈ (3/2)^(1/2) → log2(3) ≈ 1.58496 bits/step (information gain per odd step); entropy loss rate per cycle ≈ log2(3) − 2 ≈ −0.41504 bits/step (net contraction in binary length). | CONNECTION: log2(3) ≈ 1.58496 is close to the golden ratio conjugate 1.618 (φ) — deviation ≈ 0.033; the ratio 3/2 = 1.5 is a perfect fifth in music theory (base-60 harmonic), and log2(3) = ln(3)/ln(2) appears in Diophantine approximation (Baker's theorem bounds linear forms in logarithms, as cited in Tao's adelic framework). | DEPTH: 7 — The entropy interpretation is real (information loss per step is logarithmic), but the link to φ is coincidental unless proven otherwise; the adelic/Baker approach is profound but not yet resolved. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com