Flavour Ratios at Earth for Pion, Muon-Damped and Neutron Sources Under Averaged Oscillations

Flavour is the one property of an astrophysical neutrino that survives the journey in a predictable form, because averaged oscillations map any source composition to a definite composition at Earth. This paper computes that map from current mixing parameters for the three canonical source types. A pion-decay source, born at electron to muon to tau proportions of 1:2:0, arrives at 0.322:0.341:0.337 — close to, but measurably distinct from, exact equality. A muon-damped source born at 0:1:0 arrives at 0.208:0.408:0.384, retaining a clear muon-tau heaviness, while a neutron-decay source born at 1:0:0 arrives at 0.55:0.208:0.242, still electron-rich. A hypothetical additional averaging mechanism that redistributes two per cent of the flux toward equality, of the kind a long-baseline torsion-coupled phase could in principle supply, shifts the pion-source ratios by at most 2.296e-04, far below foreseeable flavour precision. Flavour will identify source classes; it will not detect such small extra averaging. The study is computed from stated assumptions, not measured.