Few-grid-point simulations of Big Bang singularity in quantum cosmology

In the context of the current lack of compatibility of the classical and quantum approaches to gravity, exactly solvable elementary pseudo-Hermitian quantum models are analyzed supporting the acceptability of a point-like form of Big Bang. The purpose is served by a hypothetical (non-covariant) identification of the ``time of Big Bang'' with the Kato's exceptional-point parameter $t=0$. Consequences (including the ambiguity of the patterns of unfolding of the singularity after Big Bang) are studied in detail. In particular, singular values of the observables are shown useful in the analysis.