Belarusian State University , Belarus

Shape-dependent observables in finite quantum dots can reflect global confinement, aspect ratio, symmetry, and dot-lead coupling in addition to finer boundary-shape variations. We apply a baseline-first assessment of these contributions to finite superelliptic quantum dots described by a spinless nearest-neighbour tight-binding Hamiltonian on a square lattice. Direct calculations cover 140 closed-dot geometries with varied size, aspect ratio, and superellipse exponent $n$, together with an open-dot transport test. Near the band bottom, the kinetic energy follows the expected $a^{-2}$ confinement scale, with a maximum relative deviation of approximately 2.12\% for $(E_0+4)a^2$ across five tested sizes. A normalized first-gap objective reaches its optimum at the same-$n$ isotropic geometry for every tested $n$, while normalized doublet splitting does not outperform a simple anisotropy reference in any of the four fixed-$n$ cases. Thus, the tested observables provide no evidence for an independent $n$-dependent spectral contribution beyond confinement, anisotropy, and symmetry lifting in the investigated range. In the open system, changing contact width gives a normalized conductance-curve distance of 0.659, compared with shape distances of 0.581 and 0.512. The baseline-first comparison therefore identifies confinement, symmetry, and contact coupling as essential reference effects when interpreting finer boundary-shape dependence in finite quantum-dot models.