Yesterday I reported that the next Rider appeared to be named Kamen Rider Gaimu, but it was potentially a troll post on 2ch. I'm here to report this morning that it was a legitimate leak. Speculation is running high that the next Rider will be samurai and Japanese mythology themed. A reputable poster on 2ch mentioned that this year's theme has "only been done once before in Kamen Rider", leading people to speculate that he's referring to Kamen Rider Hibiki.
Further fueling the speculation is the fact that the word GAIMU and the associated kanji, 鎧武, are typically used when describing sets of ceremonial samurai armor -- it comes from the word "yoroimusha", armored warrior（鎧武者）which is typically associated with samurai. For those who believe that a numerical pattern has been followed since Decade, the number six can be written with an kun-yomi reading of MU.
Lastly, there were dismissed-at-the-time reports last month of a character on the upcoming Kamen Rider Wizard movie set that was wearing a samurai style topknot and had a family crest on his belt, and was wielding two swords. There have also been rumors on 2ch that the next Rider would have a horse instead of a motorcycle, or the horse WAS a motorcycle, or something like that. An armored horse mounted samurai would not be out of line at all, and the helmet style of a typical samurai is very similar to the style of a Rider.
So, speculation is running high as to what the next Rider's gimmick could be -- whether it's different swords, magic arrows (since horse mounted archery was a big thing), or something similar. Will he give Haruto a copy of Miyamoto Musashi's Book of Five Rings when he meets him in the movie? Are you excited about SAMURIDER?