A reproducible re-examination of Beale ciphers B1 and B3: systematically closing the composite-cipher hypotheses, with methodological cautions

The three Beale ciphers (published by J. B. Ward in 1885) remain a touchstone problem in historical cryptanalysis: cipher B2 decrypts against the United States Declaration of Independence to a coherent description of a buried treasure, while B1 and B3 have resisted 140 years of attack. Building on Gillogly’s observation that B1 decoded against the Declaration produces an anomalous alphabetic run, we report a fully reproducible, open-source re-examination that (i) re-establishes the B2 positive control under a single explicit scoring framework, (ii) systematically forecloses the principal composite-cipher hypotheses for B1 and B3—Caesar, short- and long-keyword Vigenère, autokey, Beaufort, columnar transposition over all periods to 25, and the complete enumeration of all 157,248 invertible Hill 2 × 2 matrices—none of which yields English plaintext, and (iii) quantifies the Gillogly anomaly with a generative “alphabet-walking” construction model that yields a likelihood ratio of at least 100:1 in favour of deliberate construction over encryption. We additionally document two methodological pitfalls that recur in book-cipher analysis: the index-of-coincidence baseline inflation produced by a skewed key’s first-letter distribution, and the dependence of significance on null-distribution construction. Our conclusions agree with the prevailing hoax verdict for B1 and B3; the contribution is the rigour, completeness, and reproducibility of the negative result, together with a calibrated statement of residual uncertainty. All code, data, and a continuous-integration test suite are publicly archived.