Toy F — Vacuum Energy as Convergence Cost (TF2.5)

This record presents Toy F, a minimal and fully reproducible toy simulation exploring an alternative structural perspective on the cosmological constant problem. A two-dimensional lattice field undergoes iterative updates combining a contractive smoothing term with persistent stochastic fluctuations. Two energy proxies are compared: (i) a zero-point-energy-like proxy defined by the variance of the field, and (ii) a TF2.5-motivated proxy defining energy as the mean per-iteration update magnitude (a convergence cost). The toy demonstrates a strong separation between fluctuation amplitude and update-cost magnitude: while the ZPE-like proxy remains large, the convergence-cost proxy decays with iteration, illustrating how a nearly converged background may sustain fluctuations while exhibiting a small effective “vacuum energy” under an update-cost definition. All results are explicitly limited to the toy regime. The package includes raw numerical outputs (CSV), visualization figures, runnable Python code, and a LaTeX manuscript describing the model and results.