Run · Voynich Manuscript

T44 ceilings per rung: with the true key the bigram decoder fails R3 and R4 (0.482, 0.450 vs 0.488) and the element trigram decoder passes every rung (R1 0.584, R2 0.581, R3 0.544, R4 0.513, R5 0.275 vs 0.262)

test_gpu3_R1.json: the trigram code with one history class equals the bigram code to 1e-13 (likelihood, counts, Viterbi); the full trigram forward equals a plain numpy reference on two pages; EM raises the likelihood every iteration. Gold text is used here only to build the true channel; no manuscript key is chosen this way.

The element trigram model is required from R3, not R5 as planned: under the bigram decoder R3 and R4 cannot pass even if the search finds the true key. From generation 2 the pipeline polishes the best bigram states with trigram EM and decodes with the trigram Viterbi; the key-accuracy half of the gate (>= 50 %) is what keeps the coverage half honest, since the trigram decoder writes Latin-like text from almost any key. R5's bar is reachable only narrowly (0.275 vs 0.262) with the full history collapsed to 22 classes.bigram EM from truth: R1 0.518 (bar 0.483), R2 0.508 (0.487), R3 0.482 (0.488), R4 0.450 (0.488), R5 0.290 (0.262; vowel-less plaintext covers only 0.374); key 0.78-0.84 throughout. Trigram Viterbi of the true channel: R1 0.584, R2 0.585, R3 0.544, R4 0.513, R5 0.275; character similarity 0.74-0.84 (R5 0.58). Trigram EM from the truth (10-14 iterations) keeps these within 0.01, except R5 where the factored trigram (22 history classes) drifts to 0.242. A near-random key (accuracy 0.11) decoded by the trigram Viterbi still reaches coverage 0.524 (permuted keys 0.475): coverage alone cannot be the gate under this decoder0

Result

Run	Measured	Result	Against	Decision	Date
Run	Held-out dictionary coverage of the planted control decoded with the true channel and with EM started from it, against the gate bar (0.7 x the true plaintext's coverage); bigram decoder (numba lattice em) and trigram decoder (lattice gpu3)	bigram EM from truth: R1 0.518 (bar 0.483), R2 0.508 (0.487), R3 0.482 (0.488), R4 0.450 (0.488), R5 0.290 (0.262; vowel-less plaintext covers only 0.374); key 0.78-0.84 throughout. Trigram Viterbi of the true channel: R1 0.584, R2 0.585, R3 0.544, R4 0.513, R5 0.275; character similarity 0.74-0.84 (R5 0.58). Trigram EM from the truth (10-14 iterations) keeps these within 0.01, except R5 where the factored trigram (22 history classes) drifts to 0.242. A near-random key (accuracy 0.11) decoded by the trigram Viterbi still reaches coverage 0.524 (permuted keys 0.475): coverage alone cannot be the gate under this decoder	Session 12 ceiling (RUN0DCG56XXNDPT): one sign per letter 0.518, full T39 setting 0.441 with the bigram decoder	The element trigram model is required from R3, not R5 as planned: under the bigram decoder R3 and R4 cannot pass even if the search finds the true key. From generation 2 the pipeline polishes the best bigram states with trigram EM and decodes with the trigram Viterbi; the key-accuracy half of the gate (>= 50 %) is what keeps the coverage half honest, since the trigram decoder writes Latin-like text from almost any key. R5's bar is reachable only narrowly (0.275 vs 0.262) with the full history collapsed to 22 classes.

What it used and found

Lattice EM on CUDA with batched restarts, basin hopping and parallel tempering, run up a ladder of planted controls (T44)

Method

MTH

Herbal A and Herbal B paragraph text: training and held-out pages

Dataset

DAT

Latin genre texts

Dataset

DAT

Line-edge rules learned on half E (46 minimal alternations at paragraph start, line start and line end)

Dataset

DAT

Naibbe cipher tables and example plaintexts (greshko/naibbe-cipher, commit 719f2f4c)

Dataset

DAT

Token table

Dataset

DAT

Parameters

pw = 0.25, alpha = 0.05, rungs = R1 g5c; R2 h_c 4; R3 + p_copy 0.3; R4 + lam 0.25; R5 K 400 novowel 1 h_c 4 p_stay 0.98 p_break 0.9 lam 0.25, control = Pliny NH 16, period.generate seed 77, Herbal A pages, trigram = full (71 history classes) for R1-R4, factored (letters + one nomenclator class, 22) for R5 with 421 elements, bigram_em_iterations = 60, trigram_em_iterations = 20

Cite it

Mysteries Department. (2026). T44 ceilings per rung: with the true key the bigram decoder fails R3 and R4 (0.482, 0.450 vs 0.488) and the element trigram decoder passes every rung (R1 0.584, R2 0.581, R3 0.544, R4 0.513, R5 0.275 vs 0.262) [Run RUN0DCMW72CK8Y3]. https://mysteriesdept.com/r/RUN0DCMW72CK8Y3

@misc{mysteriesdept_run0dcmw72ck8y3,
  title     = {T44 ceilings per rung: with the true key the bigram decoder fails R3 and R4 (0.482, 0.450 vs 0.488) and the element trigram decoder passes every rung (R1 0.584, R2 0.581, R3 0.544, R4 0.513, R5 0.275 vs 0.262)},
  author    = {{Mysteries Department}},
  year      = {2026},
  note      = {Run, catalog key RUN0DCMW72CK8Y3},
  url       = {https://mysteriesdept.com/r/RUN0DCMW72CK8Y3}
}