Forest for the Threes

Transcription of the clues:

Two-part examples:
6 21 Arthurian villain
13 4 Authors
11 25 Backer
0 4 Lunatics
23 24 Walked on again
2 25 Woman warden
 "_ de Replay"
Dude
Sun. follower
New York baseballer
Snitch
Encountered
"Cool!"
Cat or dog
British isle
Angular meas. unit
Harry Potter's pal


First, we note that

each of the clues have three-letter answers:

"_ de Replay" - PON
Dude - MAN
Sun. follower - MON
New York baseballer - MET
Snitch - RAT
Encountered - MET
Cat or dog - PET
British isle - MAN
Harry Potter's pal - RON

Similarly,

all of the "two-part examples" have six letter answers:

Arthurian villain - MODRED
Authors - PENMEN
Backer - PATRON
Walked on again - RETROD
Woman warden - MATRON

Now, if we split those two-part examples into each of their two parts, we end up with

three-letter strings which all start with M, P, or R, have A, E, or O in the middle, and end with D, N, or T, allowing us to create the following t(h)ree:

If we then

use each string as an index, from 0-26, we see that each of the two-part examples' two parts matches up with its position in the tree (counting starting at zero, i.e. the correct way). That is, "MOD" is at index 6 and "RED" is at index 21. Doing the same conversion for each of the clue answers, we get:

PON - 16
MAN - 1
MON - 7
MET - 5
RAT - 20
MET - 5
PET - 14
MAN - 1
RON - 25

Then,

converting to letters via A1-Z26, we get:

16 - P
1 - A
7 - G
5 - E
20 - T
5 - E
18 - R
14 - N
1 - A
18 - R
25 - Y

Thus, if this puzzle were a book, it would be a

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