  Analytical evidence for the physical relevance of generalized Pauli
constraints (GPCs) has recently been provided in [PRL 110, 040404]: Natural
occupation numbers $\vec{\lambda}\equiv (\lambda_i)$ of the ground state of a
model system in the regime of weak couplings $\kappa$ of three spinless
fermions in one spatial dimension were found extremely close, in a distance
$D_{min}\sim \kappa^8$ to the boundary of the allowed region. We provide a
self-contained and complete study of this quasipinning phenomenon. In
particular, we develop tools for its systematic exploration and quantification.
We confirm that quasipinning in one dimension occurs also for larger particle
numbers and extends to intermediate coupling strengths, but vanishes for very
strong couplings. We further explore the non-triviality of our findings by
comparing quasipinning by GPCs to potential quasipinning by the less
restrictive Pauli exclusion principle constraints. This allows us to eventually
confirm the significance of GPCs beyond Pauli's exclusion principle.
