Izumi stops and looks both ways. Seeing the arrow leading left, then looking to the right and seeing stairs leading up she nods to herself. Just above a whisper she says to the others, "There are two ways to go. We go right, there are stairs upward. We go left to where the chalk arrow points. Now the writings on the wall hinted two things about paths that come to mind. 'At the start of the easy path go down', and 'look for the stairs that go up and go down'. I don't know if either are talking about this hallway, but left looks better to me and not just because of the chalk arrow.
Before moving on Izumi checks her surroundings.
(Out of Character: Listen check 13+3=16, Spot check 5+3=8, Search check 20+2=22)
You find nothing till you get to the end of the hallway to the left, you discover bloody foot prints leading down the steps going up, that turn and continue down the steps going down.
The blood looks to be around 14 hours old or so, just like the dead body was upstairs.
"I don't know the purpose, Felipe. But this sword on my back proves that I've gotten myself into something I'm not sure I want to be a part of. But this is bigger than me now, and I want to find Izumi's son."
To Izumi and Matthias: "I know it seems devious to go down, but my take on the riddle leads me to believe that we should go left, down."