A system to register same-sex partnerships opened for applications in Tokyo on Tuesday, in a symbolic step forward for a country that has fallen behind its peers on embracing diversity. The system does not offer the legal benefits of marriage for same-sex couples, but has been welcomed by LGBTQ rights groups as a small step forward. Japan is the only Group of Seven major democracy not to allow either same-sex marriage or civil unions — despite polls showing that the public is largely in favor of the change. “The introduction of the system in Tokyo is extremely positive,” said Soshi Matsuoka, the head of Fair, an LGBT rights organization in Tokyo. “But partnership is not enough. We basically want legal marriage.”