The Orthogonal Strong Force III: One Algebra for the Nucleus and the Chemical Bond

Papers I and II applied one bond, F = Rc e²/4r², to nuclear binding and to chemistry. This paper shows that the two are one algebra, and its central result is that a single operation passes registered tests in both. The conjugate return, q → −q (the same point reached the long way round), gives the zero energy step at the start of an atomic period's second pass, in six of six registered ionization series (r² ≥ 0.988), and the odd–even alternation of nuclear neutron separation energies, at 57 of 57 points. The same bond gives nuclear binding energies to 0.62% rms on 105 nuclei outside the fit, with one fitted length, and one quarter channel per covalent bond (median 0.248 over ten diatomic molecules). Both systems rest on the same objects: the half-charge pole (the bo, /bo = k¹/²); the quaternion product of two poles, whose scalar part is the Coulomb channel and whose vector part is the orthogonal (Lorentz) channel; and the vorticity η = √(energy/volume), whose cross term between two poles gives exactly Rc e²/4d. The 180° turn /bo · /bo = k (the flipped complex) makes the seven-channel proton–neutron bond; the conjugate return makes the pairing. The systems differ in how many channels a bond uses (7 or 2 in the nucleus, ¼ in a chemical bond) and in fill order. A particle set is proposed, whose unit count gives μ_p/μ_n = −1.5 against −1.460 measured.