Now that's what I'm looking for, Lee. Sort of. But you do clarify more about the nature of the ki in the various usages.
About pi quan for those who don't know:
In xing yi, I learned only the five fundamental fists. My preference is probably for shuei (?), an upward punch, more or less, but I was told that pi, the splitting fist, is the foundational fist of that system.
The appearance of pi quan:
It's basically a downward hammer fist, but it goes through a circle, the hand coming down by the waist and circling up past the opposite shoulder to drop down about sternum high directly in front of you, like all these five fists.
The problem of pi quan:
It seems weak and the feeling is that it's the most arm-dependent move of the five punches. It's hard to do it with any sense of power and it begs for muscle strength.
The "solution" for pi quan:
I suddenly felt it as a movement of ki, or I directed my ki through the inner equivalent of the outer pi quan. The circle became more important than the snap down at the end. With the circle, combined with stepping and the intermingling of your own ki with the attacker's, this could put his lower body forward while bending his upper body back over, as if you were stringing a bow, bending it back into the opposite curve. And where you have the bow well back, through use of the circle, here comes the downward solid drop of ki straight down at your feet, and it can be done with a slam.
And just before I felt pi quan in that way, I had just been thinking, actually, of a no-form application of ki/body response to an attack, and it was basically the same as described above, but with a different use of the hands. I thought, you could bend him back and slam him down by making the circle with the ki, blending his movement and leading him into this backward-bent place, then dropping the ki.
And then I thought, "Hey, maybe that's what they mean in daito ryu, dropping him at your feet."
And then I thought, "Hey, that's what pi quan is about!"
The truth about pi quan:
As Lee well explains, this is a truly multiplicit thing. Pi quan is also found in tai chi and it is also done in different ways from one type of xing yi to another. In some, instead of a fist, it's done with the edge of the open hand forward, like an axe. And as Lee also points out, it doesn't have to be downward, but can also go upward or both back and forward, which is one reason it's called "splitting".
So the first answer to my question is an uqualified "mebbe".