Cox 1966, Cox–Kanagalingam 1968, and the Scretching–JDCS–Maxwell–SQC Closure

“Building on Cox’s spectrophotometric DNA studies, this document reformulates the ratio r28/26=E280/E260 as a direct entrance coordinate in a reciprocal Cox–Scretching closure. Cox 1966 established the ratio as a useful observable for cytosine ionization and secondary-structure change, and Cox–Kanagalingam 1968 showed that denatured DNA retains measurable single-strand hypochromism, diminished by roughly 40% in 8 M urea. With Yakovchuk et al.’s later result that base stacking is the dominant stabilizing factor in duplex DNA, these observations are unified here through the Scretching Equations of Quantum Molecular Biology I–III and the Ifft–JDCS refractive-index branch. The resulting verified equations,

ρ=1.825−βs/r28/26,

Tm=138.303011−35.729302/r28/26

ηD=1.410640786−1/(127.114 r28/26)

with βs=10.8601/127.114=0.0854359079

convert the Cox ratio directly into density, melting temperature, and refractive index. A further helical-order gate is obtained from the Cox cytosine $pK$ split, ΔpKC=1.45\Delta pK_C=1.45ΔpKC=1.45, implying an ionization-suppression factor of about 28.18, and the document concludes by organizing helical order and residual stacking into a two-coordinate state space Ψ=(hc,fs), with graphs and tables verifying the internal consistency of the merged framework.”