TOKYO—Just six months ago, Mark Karpelès was sitting on top of the world. Mt. Gox, his Tokyo-based platform that had started as an exchange for Magic trading cards, had in a short time become the world's dominant platform for exchanging the new big thing—bitcoins.

Cut to a snowy February morning in Tokyo, and you find Mr. Karpelès trying to walk past a bitcoin trader holding a sign outside Mt. Gox's offices in the hip Shibuya neighborhood, asking: "MT. GOX—WHERE IS OUR MONEY?"

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