Unmasking the D’Agapeyeff Cipher (XIV, pessimistic take)

Addendum XIV (May 19): A synthetic generator now reaches the cipher’s own Simulated Annealing (SA) scores

Some findings worth recording. None of them is a decryption, and at this point the absence of decryption is the result.

The same small generator now reproduces the SA-decode property too

In Addendum XIII I noted that a two-rule synthetic generator (sample pair values from the cipher’s 18-value frequency distribution, then force the five anomalous pairs (04, 71, 92, 93, 94) to positions where index mod 14 = 13) reproduces the cipher’s residue-lattice “structural surprise” without containing any plaintext.

The natural next test was whether the same generator also reproduces what has been the more interesting finding all along: the cipher’s “quadgram-better-than-real-English” property under simulated annealing.

I generated three G1 streams (IID from the cipher’s pair-frequency distribution) and three G2 streams (IID plus the col-14 anomaly placement), then put each through the same SA hill-climb that has been run on the real cipher across many sessions. 12 restarts, 30k iterations each, joint optimization of Polybius mapping plus 14-column transposition, scored on English quadgram plus word density.

Under identical SA intensity, the real cipher’s best decode reached per-char quadgram -12.75, with 4 long English words appearing. The G1 synthetics reached -12.49 to -12.61, with 1 to 4 long words. One G2 synthetic reached -12.23, with 6 long words.

Two of the six synthetic streams produced SA decodes that score better than the real cipher’s, under identical conditions.

These streams contain no plaintext. They are pure IID samples from the cipher’s letter distribution plus one positional rule. The SA’s “tantalizing” fragments (words like STORM, ALLOW, STAND, SWING in one of them) are present at scores that match or exceed what the real cipher yields.

Three near-equally-scored decodes of the real cipher share nothing

From the inventory of 13674 historical SA-decode candidates produced by the codex framework runs in March 2026, I picked three of the highest-scoring decodes and compared the long content words appearing in each.

• Decode A (q = -9.12): WORLD, STOOD, OWNER, HARMS, LAWS, MOURNING, OFFICES, BATTLED, THEIR, WHERE, YOURS, SHOWING, WORDS.

• Decode B (q = -9.05): LORD, FATHER, GODS, HELM, FOOLISH, COULD, AFTER, DIFFER, SALLY, LINES, FORTH.

• Decode C (q = -8.67): STORM, WILLS, STAND, ALLOW, SWING.

The three-way intersection of 5+ letter content words is empty. Zero shared. Zero position-matches. Each decode tells a coherent-sounding “story” if read interpretively (Pope-flavored, religious-naval, weather-conflict) using overlapping letter statistics but completely different word content.

If these were partial decryptions of the same underlying plaintext, the expected shared-long-word count between any two near-correct decodes would be at least half of the smaller decode’s long-word count. The observed overlap is consistently zero.

Where this leaves things

The two results together close a question I have has been circling for some time. The cipher’s “tantalizing” decodes (per-char quadgram around -9, decode strings dense with recognisable English fragments) are not partial decryptions. They are pareidolia at the SA decoder’s local-optimum-finding capability. The same pareidolia is reachable from synthetic ciphers that contain no plaintext.

My reading at present is: D’Agapeyeff’s 1939 challenge is a constructed camouflage artifact. Its 17-pair alphabet was selected to match English letter frequencies under a Polybius mapping. Its col-14 anomaly placement is a deliberate construction feature, not a plaintext encoding. Its overall letter and bigram structure mimics encrypted English so closely that any SA decoder will produce English-looking output regardless of intensity, and any reader will find a “story” if they read for one. The “lost method” was a method of construction, not of encryption.

This does not prove the cipher contains no plaintext. It does establish that the cipher’s observed properties (quadgram-better-than-real-English under SA, fragment-rich decodes that don’t converge, position-non-convergent words across independent runs) are fully reproducible without plaintext. After 87 years and many independent investigations, the empirical signal now points toward absence rather than an encoded message.

The remaining work, if any, is structural: characterising the construction rather than breaking the cipher.

Maybe I’m too pessimistic. Let’s see. To be continued.

May 19, 2026