A Proposed Solution to the d'Agapeyeff Cipher (1939): Reconstruction of the Polybius Square, Rail Fence Transposition, Periodic Nulls, and Uniqueness under Structural Irrecoverability

A partial decipherment proposal is presented for the cryptogram published by Alexander d'Agapeyeff in Codes and Ciphers (1939), an open problem for over eight decades. The cryptogram consists of 196 decimal digits grouped into 98 digrams that exhibit a perfect structural bipartition. Through the reconstruction of a Polybius square with keyword MANCHESTR, an inverse Rail Fence transposition of 5 rails, and the elimination of periodic nulls at every fourth position, the plaintext candidate "now out too you" is obtained. The proposal is supported by the Index of Coincidence, Spearman correlation (ρₛ ≈ 0.61, p ≈ 0.001), and a Bayes factor BF₁₀ ≈ 30. It is formally demonstrated, via the Structural Irrecoverability Theorem, that the cryptogram contains an irreversible corruption at position 112, which restricts the space of admissible candidates to the statistically intact segment. Previous version (V1.0 — Spanish): Caillahua Mendoza, B. (2026). Una Propuesta de Solución al Cifrado d'Agapeyeff (1939): Reconstrucción del Cuadrado de Polybius, Transposición Rail Fence, Nulos Periódicos y Unicidad bajo Irrecuperabilidad Estructural (V1.0). Zenodo. https://doi.org/10.5281/zenodo.20565171