  Neutron stars offer a great opportunity to study highly compressed hadronic
matter experimentally and theoretically. However, the so-called hyperon-puzzle
arises at neutron star densities. The hyperon coexistence with other particles
in compressed matter softens the equation of state and many widely-accepted
models fail to reproduce precise observations of large neutron star masses.
Here, we propose a novel mechanism to retain the stiffness of the high density
state with hyperons by considering the explicit momentum dependence of their
in-medium potentials. Our approach modifies conventional strangeness threshold
conditions and generates new threshold effects on hyperons in high-density
matter. We demonstrate these effects within the Non-Linear Derivative model,
which incorporates baryon momentum-dependent fields based on empirical and
microscopic studies. It turns out that even soft momentum-dependent strangeness
fields do prohibit their populations in neutron star matter. The generic
momentum dependence of strangeness potentials, as modeled by the non-linear
derivative approach, is crucial for resolving the long-standing hyperon-puzzle
in neutron stars.
