A nominally treaty-compliant Japanese successor to Yamato

What might Japan build if it remained in the treaty system instead of constructing Yamato?

Probably an Iowa-like 16-inch battleship that claimed a much lower standard displacement than it actually had.

Japan's historical approach to treaty figures makes nominal compliance more likely than strict adherence. A successor to Yamato would probably use 16-inch guns and resemble an Iowa-like fast battleship. Its real displacement could approach Iowa's while the declared standard figure remained much lower. The design would preserve the appearance of treaty membership through optimistic reporting rather than a genuinely small capital ship.