Building upon the conditions for condensed matter established in Paper XXI (wavefunction overlap + thermal fluctuation suppression), this paper further derives the geometric origins of superconducting pairing, topological states, and superfluid helium. The core findings are: 1. Superconducting pairing symmetries (s-, d-, p-wave) are geomet ric projections of the relative orientations of ring vortex cones in the lattice periodic potential. s-wave corresponds to parallel/random projection, d wave to anti-parallel projection on a tetragonal lattice, and p-wave to 90◦ rotation projection. 2. The superconducting gap ratio 2∆0/(kBTc) = 3.52/ cos θeff is a direct reading of the ring geometric projection angle. The ∼ 10.56 of cuprate high-temperature superconductors corresponds to the maximum projection angle (cos θeff = 1/3), the ∼ 7 of iron-based superconductors corresponds to the inter mediate projection angle (cos θeff ≈ 0.5), and the 3.52 of BCS superconductors corresponds to the isotropic limit (cos θeff = 1). 3. Topological states: the θ = π state (axion insulator) is the necessary consequence of the ring’s topological charge Q = 1/2 being truncated at material boundaries. The phase transition critical exponent ν = 1 comes from ν = 1/(2Q), and the half-quantized Hall conductance σxy = e 2/(2h) of the axion insulator is an exclusive test.