Nuclear Binding Energies from Composite-Knot Ropelength: A Topological Model That Mirrors Quantum-Mechanical Phenomenology

We report a curious numerical observation: If atomic nuclei are modelled as connect-sums of threefoil knots with alternating chirality, the ropelength of the composite knot—a purely geometric quantity requiring no quantum mechanics—tracks the experimental binding-energy curve from hydrogen to uranium. A two-parameter fit to 50 nuclei gives R2=0.9998 coefficient of determination; 1 = perfect fit and RMS=6.9MeV (root-mean-square deviation between model and experiment), comparable to the five-parameter Bethe–Weizsäcker formula RMS=8.3MeV at less than half the parameter count. Out-of-sample predictions for Pu244 and Cf252, not used in the fit, are accurate to 0.4MeV and 8.4MeV, respectively. What makes the observation worth reporting is not the fit itself, but the range of nuclear phenomenology that emerges uninstructed from the topology: saturation, surface energy, isospin pairing, odd-even staggering, and geometric analogues of nuclear isomers all appear as consequences of the connect-sum construction, without additional assumptions. We catalogue these correspondences, assess which are structural and which may be coincidental, and identify concrete numerical tests that would distinguish the two possibilities.