Unmasking the D’Agapeyeff Cipher (XV, the recipe, not the message)

A short update, because the pessimistic take from part XIV has now been stress-tested properly, and it survived in an unexpected way.

Since the last post, the work flipped from decryption to reconstruction: instead of asking “what does it say?”, I asked “what is the simplest procedure, doable by hand in 1939, whose output is statistically indistinguishable from the published cipher?”. I searched a grammar of 720 candidate procedures on a 32-core machine, judged each one against 14 fingerprint statistics plus a heavy lattice test, and used held-out features and controls to avoid fooling myselve.

The winner is embarrassingly simple. Write a tally sheet of 18 number pairs with fixed counts. Deal them onto a 14 by 14 grid in random order, crossing each one off as you go. If a rare pair lands mid-row, swap it to the end of the row. Read off, group into fives, pad with 000. No plaintext goes in. Every statistic we know how to measure comes out matching the real cipher, including the column-14 anomaly and the lattice structure that killed earlier camouflage models.

Two honest caveats. First, this proves a message is not needed to explain the cipher, not that no message exists: I verified that old-fashioned encryptions of real text pass the same statistical battery, so statistics alone cannot decide. Second, exactly one faint trace of order survived all models: symbols three positions apart are slightly correlated. That is the fingerprint of a classic trick, writing the message down narrow columns, and it turned out earlier searches had only ever tested grid widths that divide 196 evenly. A genuine blind spot.

So I attacked it. Every ragged width from 2 to 13, both route directions, heavy simulated annealing, and, crucially, the same attack run on 60 fake ciphers generated by the recipe above, which provably contain nothing. The real cipher performed no better than the empty fakes. Its best decode used seven letters of the alphabet (real English uses about twenty) and read like SEESTREEHASH. The last thread is pulled.

My conclusion, one notch less pessimistic than part XIV: the cipher is not unsolved, it is empty. D’Agapeyeff manufactured something that looks like an encrypted message, plausibly by tallying letter frequencies from a passage of his own book and dealing them onto a grid. It would explain why he claimed to have forgotten how he encrypted it. And the lag-3 quirk, the one thing no model reproduces, is probably just the rhythm of his hand as he wrote the numbers down. After 87 years, the most personal thing anyone has recovered from the D’Agapeyeff cipher is a habit, not a message.

To be continued?