GAME OVER: BETAVEROS WINS!
Please view the comments for the solution, &c. (I'm leaving the main entry text spoiler-free for posterity).

Valid koans are 4×4 grids of letters in the word 'OXEN'.

These grids have the Buddha-nature:
NOXE NEOX EXON NNNN NNNN NNNN NNNN NNNN ( Read more... )