It should be noted that both Thinkamancy - associated with the Arkendish - and Croakamancy - associated with the Arkenpliers - lie in the axis of Fate. So far it is unclear what discipline of Magic powers the Arkenhammer (possibly Changemancy with its ability to occasionally turn walnuts to pigeons), but it would make perfect sense if that would be one of the Fate disciplines.
The Axis of Fate seems to focus on an active target's status. For instance, Croakamancy can return a character from croaked(dead) to uncroaked(undead). Presumably, Healomancy restores hit points and removes other status effects. And Thinkamancy has been shown to alter loyalty scores. Predictamancy can determine a target's future state - alive, dead, carrying around a pair of Arkenpliers.