I've followed Witch Hunter Robin for some time now, and talking with fans, it seems that one of the big mysteries of the series is exactly what time it takes place. We were sure it was set in the near future or the present; we just didn't know the exact time. :\
But I believe I've finally found the answer. I was watching the DVD when I spotted something in Episode 16,
"Heal the Pain" (spoiler!). In this episode, Robin is adjusting to her new and temporary identity as a courier
for Nagira. When she gets to her destination, she's talking to this woman at the counter, and the woman hands her
what looks like a receipt or something. I saw some numbers, paused the scene, and took note. It said
"12/2/2056". It was written in the Japanese style of dating (day/month/year), so it'd actually be written
as "2/12/2056", February 12th 2056. It was two months prior to this that Robin first arrived at the STN-J, so
WHR takes place in the winter of 2055-2056. :)
If you own the WHR "Fugitive" DVD, look at that scene closely and you'll see what I mean. ;)
