Reproduce and improve the critical coupling $K_c$ of the 3D simple-cubic Ising model by workstation Monte Carlo

The nearest-neighbour Ising model on the simple cubic lattice has coupling $K = J/(k_B T)$ and a continuous order-disorder transition at $K_c$. The 3D model has no known exact solution, so $K_c$ is known only numerically. GOAL: produce a reproducible workstation-scale Monte Carlo estimate of $K_c$ with a rigorous statistical error bar and a documented finite-size-scaling analysis (e.g. Binder-cumulant crossing of the fourth-order cumulant $U_4$, or the peak of a susceptibility/specific-heat observable), and — as the stretch goal — improve on the best published precision. Deliver a self-contained, re-runnable estimator.

Acceptance. FULLY RESOLVES: a Monte Carlo estimate $K_c = 0.221654626 \pm \sigma$ with total uncertainty smaller than the current $5\times10^{-9}$, from a documented finite-size-scaling fit, with (i) the simulation + analysis code (public repo), (ii) raw or seed-reproducible data, and (iii) a table of lattice sizes, statistics, and the extrapolation. PARTIAL (the workstation target): an independent estimate of $K_c$ consistent with $0.221654626(5)$, with a stated error bar, a named cluster/estimator (Wolff or Swendsen-Wang + Binder cumulant), finite-size-scaling plot, and a re-runnable script. Report lattice sizes, sweeps, autocorrelation times, and the random-number generator.