  Exact two-dimensional analytic wave functions for an arbitrary number $N$ of
contact-interacting lowest-Landau-level (LLL) spinful fermions are derived with
the use of combined numerical and symbolic computational approaches via
analysis of exact Hamiltonian numerical diagonalization data. Closed-form
analytic expressions are presented for two families of zero-interaction-energy
states at given total angular momentum and total spin $0 \leq S \leq N/2$ in
the neighborhood of the $\nu=1$ filling, covering the range from the maximum
density droplet to the first quasihole. Our theoretical predictions for
higher-order spatial and momentum correlations reveal intrinsic polygonal,
multi-ring crystalline-type structures, which can be tested with ultracold-atom
experiments in rapidly rotating traps, simulating quantum Hall physics
(including quantum LLL skyrmions).
