Hypothesize that White can capture ep. Proving that the position is illegal requires some retractions, followed by a parity argument. With so many open lines and bishops and queens that have moved, it seems unlikely that a parity argument will apply. However, the position is designed so that all pieces that can triangulate had not time to do so. They are all in a hurry to go back home in order to buy more retractions for White (who is running out of backward moves).

Ignoring wQ & wBf1 which never moved, it's easy to see that the captures were: bPg7xPf6, bPc7xNb6, wPaxB/Nb, wPhxN/Bg, but some doubt remains about the precise nature and location of White's captures. White has 3+6=9 pawn retractions, and it will take Black 4+2+2+1+1=10 moves with Q,Bd8,B',Pd6,Pb6 to give White a move with the unit captured on b6. This is too slow, so must get tempi from wP uncaptured on f6 first. This takes Black 4+2+1+1=8 moves with Bd8,B',Pd6,Pf6 but since bQ does not move here, we cannot bring wPa back to a2. In order to get Black light-squared bishop back in time, it must be uncaptured on b5 rather than g6. The move sequence is not quite determined, but the number of moves is known. e.g.: 1. a7-a5 a4xBb5 2. Bd7-b5 g7-g8=B 3. Bc8-d7 g6-g7 4. d7-d6 h5xNg6 5. Bc7-d8 h4-h5 6. Bf4-c7 h3-h4 7. Bh6-f4 h2-h3 8. Bf8-h6 a3-a4 9. g7xPf6 & now we have gained a few more White tempi, so can continue 9. ... f5-f6 10. Qa2-b1 f4-f5 11. Qc4-a2 f3-f4 12. Qc7-c4 f2-f3 13. Qd8-c7 a2-a3 14. c7xNb6

After all this happens, we will arrive to the following position "Nrbqkb1r/pppppppp/1N4n1/8/6n1/8/PPPPPPPP/R1B1K2R b KQk -" with Black to move, both players have made an odd number of moves, so by the parity argument to conclude that the position is illegal. A nice final subtlety is that the missing bN must reappear on g6 (not on g7 or g5, as it would be an obstacle in the path back home of bBd8). This forces the bN to reappear on a light-square (g6), making the parity argument work (the position is illegal).

Conclusion: our hypothesis was incorrect, and White cannot capture ep.

If we flipped the position (up-down, Black-White), or if equivalently we said that Black must have had the first move (half-duplex), then this position would be legal. Therefore this position is a so-called "vampire". Like the game array itself, it has no legal mirror image.