arXiv2026
We investigate finite time dynamics in nonlinear classical scalar field systems containing one ghost and one normal kinetic sector. Using a spacetime finite element formulation, we study the dependence of threshold crossing and numerical continuation times on initial amplitude, characteristic wavenumber, spectral tilt, phase structure, and spatial localization. In the quartic model, larger amplitudes generally lead to earlier growth, while higher wavenumbers and ultraviolet-biased spectra favor longer resolved bounded evolution. Smooth compact initial data exhibit a broad region with no observed growth threshold crossing over the simulated interval. A direct comparison of two Gaussian evolutions shows that enhanced low-wavenumber power can precede rapid field growth, although this observation does not establish a universal spectral-transfer mechanism. We also compare the quartic interaction with a lifted $ϕ^6$ potential. The latter gives a markedly different continuation landscape, with a broad long-converged region followed by shorter accessible terminal times at larger amplitudes. Localization diagnostics do not identify a persistent oscillon core in the selected cases. By distinguishing amplitude growth, spectral reorganization, solver-limited termination, and finite-time censoring, our results characterize a nontrivial metastability landscape without implying global or quantum stability.