[SkyFlames]

This maybe not so important but..

Spoiler:

Yuuji actually accepted the deal of giving his existence away to SoF because he told him that he was gonna stop the war between tomogaras and Flame Hazes, in that way Shana would never be in danger again and could live in peace, at this point he realized that he actually loved her. SoF letted Sakai see Shana for last time (the famous bridge scene on the OVA 4..) and there is where Yuuji confess her this (about his contract, not his love) . At this point, he wasn't an existence anymore so the common humans could not remember him anymore. Then I don't know exactly what happened so I think that is the point where Hooves starts. I maybe be wrong, if I am please correct me :P