Before getting into the actual chapter, Hagiwara includes a bunch of introductory material. I'll split this into two posts -- the first one covering the quotations from older commentaries and Hagiwara's 釈, the second with Hagiwara's 評.
I had already done some translations of the early part of this chapter, but I'm sure there are problems with them.
Old Commentaries -- The title of the chapter is taken from the words “Her residence was the Kiritsubo.” Another name is “Tsubosenzai.” This is also taken from words: “The garden plants out front were growing lushly."
The "old commentary" section is taken from the Kogetsusho. The alternate name for the chapter is found only in the Okuiri of Fujiwara no Teika; as far as I know there is no evidence outside of that work. The older commentaries had a lot of strange theories about the chapter titles; relating them to Chinese poetry or Confucian philosophy -- Hagiwara characteristically rejects all of that but because he implicitly takes the view that the entire story is the work of the single author Murasaki Shikibu, he considers the chapter titles worthy of some consideration.
Shinshaku: The origin of the name of this chapter is the fact that the Shining Genji's mother, the Haven, lived in the Kiritsubo. This is because most of this chapter recounts events related to this Haven. A certain commentary says that the name is “Tubosenzai,” taken from the words “The garden plants out front.” However, “Kiritsubo” is the more common name.
The entire story was written by Murasaki Shikibu based on a previous age. However, the reason she gave the names of previous Emperors and wrote the rest of it so that they could not be linked to a specific person was to avoid censure. Now, at this time it was lamented that the power of the Emperor had declined somewhat and that of the other nobles had increased, and she wrote this to secretly to show a time when the Emperor had more power. I will say more of this later.
I'm a little surprised Hagiwara includes this part; it's not very relevant to "Kiritsubo" itself and he's usually a little wary of theories of authorial intent like this one. I think the "names of previous Emperors" means that the Genji mentions Emperors Uda and Daigo (Engi) by name, but I'm not entirely sure. In any case this passage does not appear in the Shinshaku printed in the current Kamo no Mabuchi Zenshu; Hagiwara was working from a different text, I suppose.
Tama no Ogushi : This chapter contains events from Genji's birth to his twelfth year. At the end of the chapter it says “he became an adult” – the Kacho yosei says that these words cover three years, from his thirteenth to his fifteenth year, and that at the beginning of the “Hahakigi” chapter, he is 16. My belief is that this is wrong – “he became an adult” means that he had his donning of the trousers and thus appeared as an adult. It should not be read as covering three years. This is clear from later words that say “however, in his youthful heart [Genji] found [Fujitsubo] flawless.” Now, this chapter covers up to Genji's twelfth year, and the chronology does not connect to the “Hahakigi” chapter. In the Ise monogatari it says “Long ago there was a man who had his coming of age” – this also shows Narihira when he first becomes an adult, and then his journey to Nara is some time after that. In the same way, in this tale, the first chapter recounts up to Genji's donning of the trousers, and then the chronology begins from “Hahakigi.” The theory has also been floated that the Kiritsubo chapter is just a prologue.
I'm a little uncertain of the meaning of that last line -- the reference is to the Sairyusho, which says at the beginning of the "Hahakigi" chapter that "Kiritsubo" is just a prologue, but the meaning of that is not entirely clear.>
This first chapter, “Kiritsubo,” is the origin story of Genji. So first, the love between his father the Emperor and his mother the Intimate is recounted, and after that Genji's birth, then his donning of the trousers, then the granting of the surname Genji making him a commoner, and then his becoming the son-in-law of the Minister of the Left, and finally showing where he lives [after his marriage]. The chronology does not connect to “Hahakigi” and the later chapters. This chapter should be read as standing alone apart from the others.
Hagiwara's explanation is simpler and more direct than the others -- he wanted his commentary to be readable by "women and children" (a frequent idiom that apparently just meant "beginners") but I don't know if quoting all the previous material is much help. Perhaps he was torn between writing an accessible edition but also continuing the scholarly tradition of commentary.