Yata

A lot of people use “天空” (sky/heavens) for the center text on Narumi’s hat because that’s what’s most intuitive, especially given that a) the title of th16 is 天空璋 and b) the bulk of fanart was immediately after release and people hadn’t found all the references yet, but that has of course now been rectified (The Chinese Touhou wiki generally has a lot of information, and even the Google translated page is surprisingly readable at times).

The text reads「迷故三界城　悟故十方空　本來無東西　何處有南北 」,  which makes the visible parts “南北,” “方空,” and “西無." 

…But I wasn’t satisfied with just that, so I did some more digging!

First, Jizo statues are often adorned in red bibs (like the one Narumi wears) and knitted hats for a variety of reasons: to help ward off disease and evil, to represent generosity and goodwill towards pilgrims and travelers, to convey gratitude for the protection of children, and to help the souls of deceased children in the afterlife. 

However, as we see in this picture here, some of them are wearing distinctly out-of-place straw hats instead of warm winter hats!

This is because of the popular Japanese folktale of the Hatted Jizo, wherein a poor man goes to sell some cloth on New Year’s Eve but ends up exchanging his cloth for five straw hats after taking pity on a man trying to sell them out of season. On his way home, he spots six Jizo statues out in the cold and covers five of them with the straw hats, giving his own hat to the sixth. He goes home empty-handed but his wife isn’t upset because she takes it as proof of his generosity, and the six Jizo come to reward the kindly couple the next evening. Narumi’s straw hat covered in snow is probably an allusion to this legend. 

The hat, text and all, is also part of the traditional uniform for pilgrims undergoing the Shikoku Pilgrimage, a 1000 km route of 88 temples associated with the Buddhist monk Kōbō-Daishi. Pilgrims embarked on the journey knowing fully well that it could kill them, and wore white clothing to serve as their burial shroud should they die on their journey. According to these articles, the inscription on their hats (called sugegasa) were traditionally written on priests’ coffins. By writing the same phrases on their hats, pilgrims could use them as makeshift caskets in case they died on their journey. This practice was common enough for the inscription to be included in a pilgrimage guidebook published in 1690.

If the “Narumi was brought to life by Marisa/Alice messing around and putting the hat on her head in IN” theory turns out to be true, this ends up serving as an extra bit of irony as an item sending off the dead would end up bringing something to life, but either way it ties into Jizo’s role as a boddhisattva who works to ease the suffering of the dead and help their passage into the afterlife.

Anyhow, the actual text itself is a poem, and so you can’t translate it directly and have to interpret it, and I wasn’t feeling too confident about that. Luckily for us, this lecture here seems to know what it’s talking about!

迷故三界城 - “Bewilderment [is akin to being lost] in the City of Three Realms.”

This refers to the three realms of existence categorized by Buddhist cosmology. 迷 and 悟 are central concepts in Buddhism, referring to the states of being lost and enlightened respectively. The former is the state of living beings, and the latter is what they strive for. This line uses being lost in a city as a metaphor the standard state of all those not on the path to enlightenment meandering through the cycle of reincarnation across the three realms.

悟故十方空 - “Enlightenment [is as if there] is emptiness ten directions.”

“Ten directions“ is a poetic turn of phrase that means “everywhere,“ as it encompasses the four cardinal directions, the four intermediate directions and the vertical directions of above and below in our physical world. As Buddhist enlightenment asserts that suffering is borne from attachment to the material world, this line describes the state of enlightenment as “emptiness in all directions“ because nothing in our physical realm holds meaning, placing it in contrast to the material city of the previous line.

本來無東西 , 何處有南北 - “Originally there was no East or West, so where do South and North exist?”

This further separates the state of enlightenment from the physical realm, renouncing the divisions of direction altogether. As directions are defined by the positioning of the “self” in relation to the material world, it imposes an attachment to the physical form through the perception of worldly creatures that does not exist in the intrinsic nature of reality, but is rather a worldly preconception that must be abandoned to achieve enlightenment. This again ties back to the metaphor of the city, as it eliminates the physical directions necessary for the conception of being lost.

(Yes, all of this is conveyed by 20 characters. English really is inefficient.)

So basically, it describes abandoning worldly attachments to attain enlightenment, which pretty much is the gist of all Buddhist poetry.