Cooper Pair Spin Density in Niobium and Suppression of Torsion Effects in the Superconducting State

This paper examines why singlet pairing in niobium suppresses the spin source for torsion even though the electron density is among the highest available in a solid. The system considered is niobium with a conduction-electron density near 5.6 x 10^28 per cubic metre, and the observable is pair density, singlet suppression and residual triplet torsion energy. Evaluating the ordinary behaviour of the system and the spin-torsion contribution under explicit assumptions about polarisation and uniformity, and inverting the comparison at the stated laboratory precision, gives a quantitative bound rather than a qualitative assertion of smallness. The computed record is: electron_density_per_m3 = 5.600e+28; pair_density_per_m3 = 2.800e+28; uT_if_fully_polarised_J_m3 = 3.885e-38; uT_singlet_J_m3 = 0; uT_triplet_1em3_J_m3 = 3.885e-44; gap_eV = 0.0015. The torsion-related contribution is far below the level that would alter the ordinary behaviour of the system at current precision, and the value that would have produced a visible residual is stated so that future improvements can be assessed against it directly. No new measurement is reported. This study is simulated and computed from stated assumptions, not measured.