User blog comment:QuasarBooster/Obfuscated Bashicu Matrix Sytem in Python/@comment-35470197-20190603223832

The most accepted version of BMS now is BM2.3 (=BM4) explained here. It is still unknown whether it terminates or not. At least, the termination up to 2-row matrices (approximately \(\psi(\Omega_{\omega})\)) is verified by me. So there is no proof of termination beyond 2-row matrices, which are believed to go beyond \(\psi(\psi_{I_{\omega}}(0))\) and larger ordinals such as \(\psi(\psi_{\chi_{\varepsilon_{M+1}(0)}(0)}(0))\).