The key idea to complete the proof of the main theorem 
was found at one night when I ate a star fruit 
which I got at a wedding ceremony party of my colleague H.Terajima. 

In Japan, there is a popular computer game, where 
a man Mario or his analog dodges attacks by the enemy and go ahead, 
but he will be matchless and blow any obstruction off if he gets a star! 
(game music included 
<a href="MM/hama1-dbx_off.wav"> here </a> :-)