Torsion-Induced Neutrino Spin Conversion in a Supernova Core and the SN 1987A Constraint

A supernova core is the only environment in nature where dense, hot, neutron-rich matter and an enormous neutrino flux coexist, and neutrinos leaving such a core must cross whatever torsion the core's spin density generates. If a fraction of the core's neutron spins is aligned, the axial torsion couples a neutrino's helicity states and can convert active neutrinos into sterile right-handed ones, distorting the burst a distant observer records. SN 1987A's two dozen events matched the expected active-flavour energetics, which makes it natural to ask what polarisation of the 1987 core that agreement excludes. This paper computes the conversion in the two-state picture and reports the answer plainly: none. At a generous aligned fraction of 1e-03, the core torsion is 5.91e-28 per metre, the helicity splitting is 1.17e-34 eV, the phase accumulated over a 2e04 m crossing is 1.18e-23 radians, and the flip probability is 1.40e-46. Even at the extreme aligned fraction of 0.1 the phase is 1.18e-21 radians. The polarisation at which the flip probability would reach 0.3 — the level the 1987 signal could plausibly have noticed — computes to 4.90e+19, an impossibility, since a fraction cannot exceed one. SN 1987A therefore places no constraint on core torsion at Einstein-Cartan strength, and the paper shows the arithmetic of why: neutrino spin conversion is a resonance phenomenon in every channel where it matters, and torsion supplies neither the density of aligned spins nor a level crossing. Computed from stated assumptions, not measured.