Energy Shifts of a Spin-Polarised Torsion Pendulum in an Axial Background

This paper examines how a macroscopic spin-polarised pendulum converts a torque sensitivity into a per-spin energy limit and an axial torsion limit. The system considered is a torsion pendulum carrying of order 10^23 polarised electron spins, and the observable is pendulum torque and the corresponding energy shift per spin. 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: N_polarised = 1.000e+23; torque_sensitivity_Nm = 1.000e-16; energy_per_spin_J = 1.000e-39; torsion_bound_per_m = 3.163e-14; dipole_energy_J_at_bound = 1.000e-39. 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.