HEP
In the literature: open
Why are there exactly three fermion generations?
In plain words
Experiments show three light neutrino types and three sets of quarks and leptons, and a fourth ordinary copy is ruled out. Why three, and not one or four, is unknown.
Precise statement
LEP Z-width data give $N_\nu = 2.9963 \pm 0.0074$ light neutrino species after the 2020 luminosity correction (Janot and Jadach), and Higgs production rates exclude a fourth sequential chiral generation. An answer is a principle (anomaly cancellation in an extended gauge group, string compactification topology, or a symmetry argument) that requires $N_{\mathrm{g}} = 3$ and makes a further testable prediction.
What would settle it
A framework deriving $N_g = 3$ whose additional predictions are verified experimentally.