What might Japan have planned after Yamato?

What was the Imperial Japanese Navy considering after the Yamato class?

Probably an even larger design, whose disclosure might have triggered an American building race and bought Japan time.

The relevant Japanese records did not survive, so the successor design remains uncertain. The likely direction was an even larger battleship, and possible British or other responses quickly turn the question into an international building race. Revealing the concept might have forced the United States to reconsider, pause, or enlarge ships already under construction. In this strategic reading, the threat of the design could have bought Japan time even if the ship itself never became decisive.