379

379 is a number that repeatedly appears in Exit/Corners. According to Aether's supposed clairvoyance, this number is significant to the game somehow.

Chapter 1
Though hard to discern and appearing for only a moment, Aether and Ink's room number is 379.

Ink mistakes the date, which is supposedly "3/19", for "3/79". Aether later implies in Chapter 16 that she mistook it, too.

Chapter 2-5
None are found in these chapters.

Chapter 6
While this could be a coincidence, in the hint, the number 373.15 is given for Kelvin, while in the puzzle itself, the corresponding slot only says 373. If one adds the last 3 digits of the extended number together, one gets the number 379. However, it could simply be explained by the fact that, since Sent had more space in the hint, he could afford to be more precise with the number.

Chapter 7-11
None are found in these chapters.

Chapter 12
In the default layout of puzzle, the first column consists of a 3 of hearts, a 7 of spades, and a 9 of diamonds.

Chapter 13
None are found in this chapter.

Chapter 14
In the puzzle, one of the arms on the right-hand side has a weight of 37.9.

Chapter 16
A picture appears with the number painted on it, with the 7 in red and slightly tilted.

379 appears in the default setup of the puzzle, in the second row of the numbers section. Plus, the default date is March 19th, the supposed date of Exit/Corners and also the number Ink had earlier mistaken for 379.

Chapter 18
The aforementioned picture from Chapter 16 appears again as they backtrack.

The default arrangement of the first puzzle includes 379 in the middle row,

The default arrangement of the second puzzle includes 379 in the right column, as does the third.

Chapter 19
None are found in this chapter.