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For proof of what you are explaining, the "original WiP thread ..." is looking sufficient; I had a question here, whether you needed to actually have submitted the game at the other jam so I checked the wording and it says "[...] finish a game you started or remade at another Jam this summer" but also, in the rules "must have been entered into another jam".

So I think strictly speaking you should have submitted your game at the other jam first (did you?), but I'll be putting the emphasis on quality here not nit-picking; so as long as you could demonstrate (as explained by you) that you participated in that jam your entry will qualify.

It's a jam I strictly entered on the forums, I do know that as of late they've had itch.io jam pages for it now--but I do not think I had an itch.io account at the time, so I entered it like most others do by making a WiP thread in the NaNoRenO board since the jam's been going on annually I think before itch.io even started so a lot of us enter it that way, some even have surprise entries by posting a complete game made within the time-span they never announced. But I did announce mine. 

This was my entry thread in question; https://lemmasoft.renai.us/forums/viewtopic.php?f=50&t=42807

And in the pinned topic, "NaNo 2017 Games by Genre", which shows every game--finished or not--entered into the jam by genre to their WiPs, you'll find mine "An Encounter ~In The Rain~" by the genres "Friendship" and "Linear"; https://lemmasoft.renai.us/forums/viewtopic.php?f=50&t=42982