Is "of the kitten" in "the paw of the kitten" a complement to the NP or an adjunct to the DP?

I'm drawing a tree for "the paw of the kitten" (from chapter 7 of Andrew Carnie's Syntax: A Generative Introduction). This chapter is "extending X-bar theory", so please keep that in mind when answering (i.e. please don't confuse me with too modern / alternative theories).

According to Carnie, a PP with "of" is usually a complement, and some tests would seem to confirm that in this case:

• Adjacent to head: *the paw which is white of the kitten (cf. [the paw of the kitten] which is white)
• No two "of"-phrases allowed: *the paw of the kitten of the dog (intended: the paw which is of both the kitten and the dog)

So that would give the first tree below.

However, on the other hand, if I try to apply some constituency tests I want to take "the paw" as a constituent:

• You can insert a pause at "the paw — of the kitten" but not "the — paw of the kitten"
• Conjunction of "paw of the kitten" fails: *the paw of the kitten and leg of the horse (should be: the leg)
• Stand-alone: "What is of the kitten? The paw", but you cannot have "paw of the kitten" stand alone
• Movement: "Of the kitten is the paw" is kind of OK, but you clearly cannot move "paw of the kitten"

So that would give the second tree below.

How do I decide between these two options? I don't think the PP can be a complement to the D, because the complement position is already taken by "paw".

I don't find your constituency tests convincing, so I would go with the complement analysis unless there are other arguments against it.

You can insert a pause at "the paw — of the kitten" but not "the — paw of the kitten"

I'm not familiar with this constituency test, but doesn't it definitely have exceptions? There are many morphemes analyzed as clitics that are phonologically attached to the adjacent word but not necessarily more closely bracketed with it than with other words in the phrase in terms of syntactic structure. The being cliticized with paw seems like an adequate explanation of why a pause would not be inserted after it (I don't think it's actually impossible for a pause to come here in certain circumstances).

Conjunction of "paw of the kitten" fails: *the paw of the kitten and leg of the horse (should be: the leg)

"The paw of the kitten and leg of the horse" is not strongly unacceptable to me. I prefer "The paw of the kitten and the leg of the horse", but I think that could be for other reasons (e.g. maybe "the" tends to be repeated unless the conjoined n-bars/nominals are seen as associated or comparable). For comparison, here is a sentence I found with conjunction in a similar context--I find it acceptable:

Maximum contamination was found on the right arm of the operator and left arm of the assistant.

Stand-alone: "What is of the kitten? The paw", but you cannot have "paw of the kitten" stand alone

Movement: "Of the kitten is the paw" is kind of OK, but you clearly cannot move "paw of the kitten"

Both of those seem to me to have slightly different semantics than "the paw of the kitten", and to sound considerably less natural. You cite Carney as saying that a PP with "of" is usually a complement; these examples seem to show only that it is not impossible to use it as an adjunct.

• Many thanks for your thoughts. I went a bit too far with the "pause" test indeed. I based this on a greyed-out block in Carnie (p. 65 in the 2nd ed.) where he discusses Merrill Garrett's 1967 PhD dissertation. They do a test where people listen to a recording of "In her hope of marrying An/na was impractical" and "Harry's hope of marrying An/na was impractical", where a click is placed at the slash sign. People perceive this click as before "Anna" in the first sentence but after "Anna" in the second, at the edges of the constituents. My test was based on that, but it's not really the same. Jul 13 '20 at 7:01
• Could you explain one thing to me though? You write that you prefer an analysis where "of the kitten" is a complement, because the constituency tests are not convincing. I see your points. But then in the last paragraph you write that this example shows that of-phrases may also be adjuncts, in some cases? Jul 13 '20 at 7:03
• Could you have a look at that final question, please? Thanks! Jul 17 '20 at 8:59