  Recently (May-November 2013) highest energy neutrino events have been
presented by ICECUBE. Most (21) of all these (28) events are cascades shower
whose flux exhibits a sharp hardening respect other lower energy atmospheric
neutrino component, events suggesting an injection of extraterrestrial
neutrino, mostly nu e, nu tau, making cascades. ICECUBE claimed that a
component (10:6+5:0 3:6), a third, of these events must be a trace of expected
downward muons and-or atmospheric neutrinos (muon track dominated): The
probability that this scenario occurs is very poor, about 0.1- 0.5%. The
paradox might be mitigate as we suggest if nearly all of the 28 events are
originated by extraterrestrial sources arriving to us in de-coherent states. At
first sight also a partial solution may rise if highest energy events at E nu >
60 TeV ( 17 showering versus 4 muon tracks) are mostly of extraterrestrial
nature. However this solution leaves problematic the earlier 30 - 60 TeV energy
region, whose 8 showers versus 3 tracks is in tension with most nearby
atmospheric neutrino signals, by a sharp difference at TeV energy ruled (as
shown in Deep Core) by ten over one neutrino (muon) events over showers. This
puzzling (fast) flavor transition from atmospheric nu muon flux at TeV to tens
TeV showers and muon neutrino absence has deep consequences. Few cascades
shower events in Antares might also test the nu flavor changes above TeVs up to
a rare one at few tens TeV signal. Higher energy EeV tau air-shower induced by
UHE nu tau within mountains or Earth skin while skimming terrestrial ground as
AUGER arrays might be still rare, but the correlated horizontal upward PeVs tau
air-shower may soon shine into ASHRA crown telescopes at mountain edges by
their Cherenkov flashes.
