|1:A pheasant came from Heaven to lower country to see how Heaven's agent, Ame-no-Waka-hiko was working.||The bird stayed at a Katsura tree||Kojiki and Nihon-shoki|
|2: When Hiko-HoHo-Demi visited the Sea God||He waited on (or by) a Katsura tree||Kojiki and Nihon-shoki|
|3: When the god(des) of Moon visited another god of the lower country||It waited by a Katsura tree||Fudoki of Yamashiro|
|As above seen, the Katsura tree is mentioned when a god or important person visited from upper country to lower country.|
|Hito Koto Nushi Shrine in "Katsura-gi" (N.B. "gi"="ki"=a tree) is said to be the place||where the God descended, according to the shrine's description. Here, there is another example of the "Katsura" and "descent" being connected.|
If I stop here, I'd have just presented that the tree has some association with descent, which, as far as I know, is the first finding.
If the stories in the above table are of Jomon people spoken in Jomon language, "ranke" at/by a "ranko" tree is an interesting phonetic pair.
The road is called "Ran-Katsura" at Nitta and "Dan-Kazura" in Kamakura.
Ran-Katsura or Dan-Kazura has no sensible meaning if the both syllables are to be understood only in Japanese. They can be comprehensive if "Ran" came from Jomon and "Katsura" came from, say, Yayoi or invading (and mixed) people; and two were combined. "Dan" is easy to be considered same word as "Ran" with different pronunciation either by time or by geographical distance.
It is not certain whether Kamakura's "Tai-Ko" bridge can be traced back to the same meaning, like Tai-Ko came from Rai-Ko, essentially the same meaning as Ko-Rai. Many believe that the Kamakura bridge was named after its shape, that is, looking like a drum [= Taiko]. I'm questioning it.