The D'Agapeyeff Cryptogram (1939) : Anatomy, Reconstruction of a Solver, and Statistical Assessment

This report documents a computational cryptanalysis attempt on the 196-symbol challenge cryptogram published by Alexander D'Agapeyeff in 1939, at the end of the first edition of his book Codes and Ciphers (Oxford University Press). The cryptogram has never been solved. The report retraces the entire research process : the design flaw that invalidated an initial solver, the reconstructed architecture, and the systematic search that followed. Four classical cipher families, labeled A through D (A: substitution, B: columnar transposition, C: Fleissner grille, D: double transposition), plus a Four-square digram cipher, were tested under three linguistic hypotheses (English, French, transliterated Hebrew), using a calibrated quadgram language model and simulated annealing. A central methodological contribution is a null-baseline calibration methodology : every promising result is checked against the same search run on a randomly shuffled version of the cryptogram, at equal trial volume, to distinguish genuine signal from statistical artifacts arising from testing very large numbers of combinations. At the project's closure, methods A through D reached guaranteed 100% coverage over two independent systematic sweeps (main run and null baseline), with no statistically distinguishable signal detected. The Four-square cipher was covered to 20.9% of its search space before the project was closed for lack of further computing resources, again with no signal found. The report documents this rigorous negative result in full, together with the methodological lessons drawn from it : calibration pitfalls, defensible hypothesis-space extension, the limits of a numeric score as evidence of linguistic coherence, and the validation of new search mechanisms. The full code, corpora, and raw results underlying this report (millions of logged combinations) are published separately on Zenodo for transparency and reproducibility.