Thanks, fixed.

White koans:
AR       RO
NE       RR
NO       SORTH
NORTH    SOURTH
ONO      ZONNE
OR
ORTH
Q
QVW
R

Black koans:
AC            OS       ZNE
AD            OTH      ZONE
AG            OUTH
AO            SO
BDP           SOUTH
CEFGHIJKLM    V
EAST          W
MO            WEST
O             XYZ
OO            ZN

Quote from: Proxima on Today at 03:56:53 AMWhite koans:
AR       RR
NO       SOUTH
[...]

SOUTH is suddenly white here. It's still correctly black, too. SORTH is the missing white koan.

-- Simon

The outermost peel of the onion has come off.

NE
ZN
ZNE
ZONNE

-- Simon

Added the counterexample ZONE.

White koans:
AR       RR
NO       SORTH
NORTH    SOURTH
ONO
OR
ORTH
Q
QVW
R
RO

Black koans:
AC            OS
AD            OTH
AG            OUTH
AO            SO
BDP           SOUTH
CEFGHIJKLM    V
EAST          W
MO            WEST
O             XYZ
OO            ZONE

AKHTBN iff it contains an R or a letter at ±4 from R (which are N and V).

This would be the only pattern I see. Everything else is an arbitrary set of letters that doesn't seem to make nice words, or be at nice distances from each other. If that's not the solution: Test the following three ...

V
Q
W

... and then guess: AKHTBN iff it contains at least one of: R, N, or a white one of those three (Q, V, W).

-- Simon

You accidentally counterexampled yourself 

White koans:
AR       SORTH
NO       SOURTH
NORTH
ONO
OR
ORTH
QVW
R
RO
RR

Black koans:
AC            OS
AD            OTH
AG            OUTH
AO            SO
BDP           SOUTH
CEFGHIJKLM    WEST
EAST          XYZ
MO
O
OO

AKHTBN iff it contains at least one R or at least one N (or both).

BDP
QVW
XYZ

-- Simon

White koans:
AR
NO
NORTH
ONO
OR
ORTH
R
RO
RR
SORTH
SOURTH

Black koans:
AC            OTH
AD            OUTH
AG            SO
AO            SOUTH
CEFGHIJKLM    WEST
EAST
MO
O
OO
OS

R
O
AR
AO
CEFGHIJKLM

-- Simon

White koans:
NO
NORTH
ONO
OR
ORTH
RO
RR
SORTH
SOURTH

Black koans:
AC
AD
AG
EAST
MO
OO
OS
SO
SOUTH
OTH
OUTH
WEST