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This paper constructs two superconducting pairing models on a doped Kitaev honeycomb lattice by deriving microscopic kernels from fundamental principles rather than assuming them. Model 1, driven by a flux-sector selection rule, yields an odd-parity triplet pairing with a bond-locked anisotropic $\mathbf d$ vector, while Model 2, based on a chiral phonon selection rule, results in an even-parity $d+id$ singlet pairing. A general theorem reveals that on odd-fold bond stars, chiral form factors enforce parity-alternating singlet-triplet composite states, with the Chern number determined by the dominant on-shell component.
Superconducting pairing models are constructed from first principles on a Kitaev honeycomb, revealing parity-alternating singlet-triplet composite states driven by a bond-local glue.
We construct two superconducting pairing models on doped Kitaev honeycomb, whose microscopic kernels are derived rather than assumed. Both are driven by a bond-local glue neutral between the even- and odd-parity pairing channels; the chirality--parity linkage is set by bond-star geometry, not by the microscopic glue. (i) Model~1(odd-parity sector): the kernel follows from the flux-sector selection rule of the pure model, fixing its component-diagonal, nearest-neighbor separable, rank-one-per-bond form, with $w_\alpha=J_K^2\chi_\alpha\propto r_\alpha m_\alpha$, where $m_\alpha$ follows from the Hellmann--Feynman theorem and $r_\alpha\simeq0.24$ is computed numerically. The spin-vertex state is a unitary triplet with a bond-locked anisotropic $\mathbf d$ vector; its gap is a Gram sum of bond sines, so nodal directions are fixed by geometry. (ii) Model~2(even): the kernel is fixed by the $C_3$ little-group selection rule of a zone-corner chiral phonon, up to a Cooper-channel extension whose momentum constraint we state explicitly. The charge-vertex pairing is a $d+id$ singlet: the parity decomposition $f_\pm=g_\pm+p_\pm$ projects onto $g_\pm$, so chirality is slaved to the phonon polarization, with $C=\pm4$ and $\kappa_{xy}/T=2\kappa_0$. Reversing the pump helicity reverses the Chern number, Kerr rotation, and thermal Hall sign. (iii) General theorem: on odd-fold bond stars, the angular-momentum ladder of a single-star chiral form factor alternates in parity. Every chiral state selected by such a bond-local form factor is a geometrically enforced singlet--triplet composite with universal amplitude ratios ($n=3$: $d\oplus p$; $n=5$: $g\oplus p$ or $d\oplus f$); coherent doubled-star combinations can restore parity purity. The Chern number of the mixed state follows the dominant on-shell component across a topological boundary. The spin glue drives $C=\pm2$; the charge kernel $C=\pm4$.