These results represent the culmination of the solution for the historical problem of the contamination by matter effects in the discrete CP, T, CPT asymmetries for neutrino propagation. Using that vacuum is CPT-symmetric and matter is T-symmetric, the goal is accomplished in terms of a basis of three independent components: genuine CPT-even, matter-induced T-even, interference CP-even. Independent of the theoretical framework for the dynamics of the active neutrino flavors, we prove the Disentanglement Theorem
A(CP)=A(CP,T)+A(CP,CPT), A(T)=A(T,CP)+A(T,CPT), A(CPT)=A(CPT,CP)+A(CPT,T)
for the three independent experimental asymmetries (left-hand side) in terms of the three components (right-hand side). For even a T-symmetric matter, A(T) is -contrary to general belief- affected by matter due to quantum interference.
For the effective Hamiltonian written as the sum of free mass propagation plus the matter potential for electron-neutrinos, the three components have definite parities under the baseline L, the matter potential "a", the imaginary part sin(delta) of the PMNS mixing matrix and the hierarchy "h"=+-1 in the neutrino mass ordering: A(CP,T) is odd in L and sin(delta) plus even in a and h, A(CP,CPT) is even in L and sin(delta) plus odd in a and h, A(T,CPT) is odd in all L, sin(delta), a and h. The last interference component contains then
terms like a.sin(delta).
The independent measurement of the three asymmetries could only be made in neutrino factories and atmospheric neutrinos. For present terrestrial accelerator sources of muon-neutrinos and antineutrinos, the two components of the appearance CPV asymmetry A(CP) can be disentangled by either baseline dependence (HKK) or energy dependence (DUNE). At the DUNE baseline, the higher energy region above the first oscillation node provides a dominant matter-induced A(CP,CPT) component
and the sign of the experimental asymmetry A(CP) gives the hierarchy in the neutrino mass ordering. On the contrary, there is a "magic energy" E around the second oscillation maximum in which the fake A(CP,CPT) component has a first-rank zero whereas the genuine A(CP,T) component has a maximum (proportional to sin(delta)). With a modest energy resolution Delta E ~ 200 MeV an effective zero remains in the matter-induced A(CP, CPT).