On Heuristic Structure Extraction in Under-Specified Transposition Ciphers: A Case Study on the Diagapeyev Cipher

This study investigates a heuristic optimization framework applied to the Diagapeyev Cipher, modeled as an under-specified transposition cipher with unknown structural parameters, including grid size and permutation rules. We formulate the problem as a combinatorial optimization over permutation matrices and apply large-scale stochastic search guided by a trigram-based statistical language model. To evaluate the scoring function, an empirical null distribution is constructed using randomly permuted configurations under identical structural constraints. A 6x6 permutation state with a log-score of 15.84 is observed from the heuristic search procedure. Importantly, this result does not imply recovery of a unique historical plaintext. Instead, it reflects the behavior of a statistical scoring function over a high-dimensional combinatorial search space. These results suggest that structured linguistic patterns may emerge as an interaction effect between the scoring model and search dynamics in permutation space, rather than as evidence of successful decryption.