The McCaffer-Bovill activation potential V (θ) = V0 sin2(θ/2) is established as a comprehensive framework for torsional physics through seven results. (1) A Fourier uniqueness theorem proves sin2(θ/2) is the unique leading-order rotational cost function, explaining its independent appearance across ve physical domains. (2) A variational principle E(n) = V0sin2(π/n) + Ubb(n) using experimentally known DNA backbone geometry predicts the equilibrium periodicity n∗ ≈ 10-10.5 base pairs per turn from first principles,without fitting to the observed value. (3) Connection to DFT-computed base-stacking energies constrains V0 independently of calorimetric calibration. (4) The parameter-free energyratio ∆G(B→Z)/∆G(B→A)twist = 1.7684 is presented with a complete experimental protocol for definitive testing. (5) The 90◦ threshold is shown to correspond to the criticalpoint s = 1 of the Zimm-Bragg helix-coil transition, connecting geometric classification tostatistical mechanics. (6) Falsifiable predictions of helix stability and instability are made forspecific untested systems including γ-peptide foldamers, polyallenes, and modified collagenmimics. (7) Engineering design rules are derived for torsional systems, including qualityfactors, coupling efficiency bounds, and thermal stability requirements. The golden ratio φenters functionally as the torsional spring constant κtwist = V0φ/4 at B-DNA's equilibriumangle, determining thermal twist uctuation amplitudes and the stability margin below theself-stabilisation threshold. Seven predictions are confirmed or proved, two are consistentwith data, one is partially confirmed, and three await experimental testing. Zero predictionsare falsified.
Alastair McCaffer (Sun,) studied this question.