Triangled: Sorry if I misunderstood your point. I agree that the joist hangers indicated that the joists appeared to be simply supported at the exterior edge of the balcony. If the joists are bearing on the 3x rim board, what supports the rim board?
Skeezix
I think "lsmfse" is right. The intermediate joists look greener than the cantilevered joists and the deck boards look pretty new.
Good to see some white metal flashing along the wall. Better if it turned down and had spaces to allow drainage and drying between the flashing and the deck boards...
jmy,
In addition to good advice from Ron and VoD, here are a few more ideas for your consideration:
1. You may be able to find out more about the original post-tensioning by calling local subcontractors and suppliers. Even if the p-t was furnished and installed by a contractor from out of town...