= Solution
In $\tau^-\to\ell^-\bar\nu_\ell\nu_\tau$, charge and missing <four-momentum> show an invisible neutral component beyond the visible charged <lepton>. The distributions are consistent with three-body <V-A interaction> decay; hadronic modes such as $\tau^-\to\pi^-\nu_\tau$ instead have two-body missing-mass kinematics. Production and decay accounting assigns $L_\tau(\tau^-)=L_\tau(\nu_\tau)=1$ and their antiparticles minus one. Searches for wrong-flavour and neutrinoless channels constrain violations. These observations establish a useful approximately conserved tau-family number in ordinary interactions, rather than proving an exact law from missing <energy> alone.
To establish that the invisible particle is distinct from $\nu_e$ and $\nu_\mu$, combine decay evidence with the absence of unsuppressed tau production by conventional electron- and muon-flavour beams, and direct <tau neutrino> <charged current> interactions. <DONUT> observed the short displaced <tau lepton> decay in nuclear emulsion after a neutrino interaction. <Observation of Tau Neutrino Interactions by DONUT Collaboration>[DONUT first direct tau-neutrino interaction report]{ref} <Neutrino oscillation> means individual family numbers are not exact conserved quantities during propagation, even though they are an excellent approximation for these local decay assignments.
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