after watching ep10 with eng subs, i guess we have a clearer picture that there are 2 core organizations... Alice (rep. by the omega symbol) and "Teacher" (rep. by the sigma symbol).
the flashback scene in 2010 at the prison... Detective Ko was already a time traveler since then? he was tasked to kill Tae Yi but did not know that Park Sun Young was actually Tae Yi in another name, thus he was shocked to see Jin Gyeom and his mom's photo in the living room. i'm thinking he took on fostering Jin Gyeom out of guilt and not cos of the instructions from the sigma organization, and his family grew close to him after all these years as well. (i love the heart symbol after Jin Gyeom's name in Detective Ko's caller id)
it seems like something critical might happen to his wife really soon, Detective Ko should already know the date is approaching if he had been a time traveler.
(cancer? health issues? cos they seemed to over emphasize in this ep, and he said that's the only way for him to save his wife in ep11 preview)
Jin Gyeom's supposed death on 15 Oct 2020 in his house might have taken a new route, since Tae Yi deleted the photo at the amusement park (linking this back to the Butterfly Effect theory that Director Seo O Won).
AHHH... @flutterby06 thanks for reminding on the Chuseok holiday... i guess, i have to celebrate mine eating mooncakes and procrastinating about 7 additional days to wait for the next ep!