Endless Paradigm

7 (am i close?)

0011001100111010 is next in sequence - and is the 8th sequence.
however the binary in hex looks like this

3031 3035 (difference being 4)
3131 3136 (difference being 5)
3232 3238 (difference being 6)
333A (last number hanging is number 7 but calculated 8th to work it out)

am i overanalysing this? and i don't see the message being tied to this but i have a very rigid mind.

closest i can get is recover - presumably related to partitions. (0x6?)

12337 =16
12341 =11
12593 =20
12598 =25
12850 =16
12856 =22
13107 =12

R 1
Y 2
E 3
H 4
E 5
T 6
E 7
R 8
A 9
E 10
V 11
R 12
E 13
H 14
W 15
E 16
S 17
E 18
M 19
O 20
R 21
R 22
D 23
U 24
C 25
R 26
E 27
S 28
H 29
E 30
H 31
T 32
E 33

evocerr
rrecove
shift one place left and you get recover.

did you perhaps get the order wrong or is that part of the puzzle?