Formation and First Turnaround of an Ultracompact Breathing Scalar Shell with a Plateau Potential

Spherically symmetric 3+1 solver for a minimally coupled real scalar field with a saturating plateau potential V(phi) = rho_sat tanh^2(phi/phi_star), in polar-areal gauge with polar slicing, together with the production run matrix, raw diagnostics, figures and reproducibility tests underlying Section 6 of the accompanying manuscript. The deposit contains the evolution and constraint solvers with a driver whose physical and numerical parameters are supplied entirely from the command line or a JSON config; nine production runs covering three initial amplitudes and three native radial resolutions, each with a time series, radial profile snapshots and a manifest recording every parameter, the SHA-256 of every solver module and output file, and the software environment; the figures and a machine-readable table of every number quoted in Section 6; and a convergence test of the Hamiltonian-constraint solver against a tight-tolerance reference integration. Every figure and every number in Section 6 is produced from the deposited data by the figure script; no value is entered by hand. The verification script checks code and data hashes against the run manifests, re-runs a short reference configuration, and rebuilds the figures in a scratch directory, requiring the resulting numbers table to be identical. The complete matrix regenerates from source in a few minutes. Two criteria, fixed before analysis, bound the interval over which the central diagnostics are used: fractional drift of the Misner-Sharp mass below 1e-3, and self-convergence of the central proxy below 0.05 of the potential plateau. The mass drift is shown to be numerical rather than physical, converging away under refinement at close to second order. This version supersedes the figures and Section 6 numbers of earlier versions of this record, which are not reproducible from any available code and should not be used. A previously circulated vectorised implementation of the constraint solver returned u = 0.861 instead of 1.000 in the first grid cell and did not converge under refinement, an error located exactly where the central diagnostics are evaluated. The implementation deposited here is second-order convergent and agrees with a reference integration to machine precision at the axis.