Parameter-Free Helicity Selection in Chiral Oligomers and Nanotubes: Closed Pauli–Bohm Waveguides, Connectivity Rules, and Shot-Noise Signatures

Room-temperature chiral induced spin selectivity (CISS) in light-element organic oligomers and carbon nanotubes consistently exceeds perturbation estimates based on atomic carbon spin-orbit coupling (meV) by two orders of magnitude. Here we formulate a unified, parameter-free quantum waveguide theory for discrete N-gon ring chains and continuous chiral nanotubes grounded in Pauli–Bohm mechanics and boundary-locked Darboux frames. By treating electron spin natively as an invariant planar action quantum |S_p| = |δr × δp|/(4π) = h/(4π) anchored via radial wall contact δr to the concave inner boundary of a closed cross-section, single-valued loop closure locks spin handedness (helicity H = ŝ · p̂) directly to structural chirality (ξ = ±1) at the kinetic hopping scale (J ~ eV). This (P-odd, T-even) coupling preserves Kramers degeneracy at rest while flipping lab-frame spin upon bias reversal. On discrete hexagonal (N = 6) waveguides, Landauer–Büttiker scattering yields strict topological design rules: symmetric para (1,4) connectivity passes opposite radial spins equally (0% CISS), whereas asymmetric meta (1,3) connectivity extinguishes one chiral eigenbranch, achieving 99.8% eigenmode purity by the second ring and saturating longitudinal bond polarization at the geometric ceiling 3/√13 ≈ 83.2%. In chiral nanotubes of nanoscale radius R ~ 3 Å, petahertz inner-wall twist rates generate sub-eV chiral cutoff windows while a 900:1 timescale separation between attosecond bond transit (~0.18 fs) and room-temperature lattice vibrations (~160 fs) renders single-ring locking stroboscopically deterministic while thermally damping multi-loop Kramers echoes. Furthermore, Pauli arrival spacing (Δt = h/(T eV) ≈ 41 fs at 0.1 V) leaves each ring unoccupied over 97% of the time—preempting empirical Hubbard-U fitting—and predicts a magnet-free quantum shot-noise Fano factor dip to F = (1 − P²)/2 ≈ 0.004 at conductance G = e²/h.