Phi-Convergence in the DNA Double Helix: The Molecule of Life as a Necessity Recursion Structure

DNA’s double helix has dimensions encoded in consecutive Fibonacci numbers: 34 Å turn length, 21 Å width, 22 Å and 13 Å groove widths. The primary ratio 34/21 yields phi-deviation δ = 0.000626 — lower than carbon’s sp3/sp2 bonding ratio (δ = 0.016, Paper 19). Fibonacci Causal Loop Theory proposes this reflects 3.8 billion years of necessity recursion pressure under evolutionary selection — the longest optimization run of any known molecule. The same Fibonacci pair (34, 21) appears in botanical phyllotaxis (Paper 20), reflecting the same recursion operating under sequential growth constraint at different scales. Prediction 21 is formally stated: phi-deviation of DNA helical ratios will vary with DNA form and GC content, testable against RCSB crystallographic data. Paper 21 in the FCLT series.