Emerging methods for an unlabeled symbol sequence: a survey for the Voynich program

Written from the collected material in afcf4c0f279d30bfe.full.md (web searches and page fetches made 2026-10-22) plus six verification calls. Every citation carries a tag:

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0. Scope, constraints, and what is already done

Data. ~37,000 word tokens in EVA transliteration (~190k glyph characters, ~8k word types), with line/paragraph/page/quire structure, section labels (herbal, astronomical, biological, cosmological, pharmaceutical, recipes), Currier A/B, Davis's five-scribe assignment, label vs paragraph text, and ~500 figures. The ZL (Zandbergen–Landini) transliteration marks uncertain word breaks separately from confident ones; Rozanova & Temerev's 2026 preprint (arXiv:2608.17096, VERIFIED) reports that those uncertain separators behave as within-word junctures and are physically narrower. Any method below should therefore be run under at least two unitizations: EVA glyphs as given, and a merged-unit alphabet (the program's BPE merge curves give a principled cut point; Zattera's 12-slot alphabet, CEUR Vol-3313 paper10, VERIFIED, is an alternative).

Compute. One machine, 2 CPU cores, no GPU, outbound HTTPS only through a restricted proxy. Consequences:

• Anything that trains a model with more than a few million parameters, or that runs inference with a large pretrained vision/language model, is out unless weights are already on disk. CLIP, DINOv2, SAM, TrOCR, LayoutLM and any LLM fall here. Their weights (300 MB to several GB) come from Hugging Face or Meta CDNs that a restricted proxy may block, and CPU inference on 500 figures is slow but possible only if the download succeeds. Treat these as conditional on a one-time weight download.
• Classical and small-model work is fully feasible: n-gram and HMM fitting, PELT/BOCPD, adaptor grammars, Morfessor, Brown/IB clustering, word2vec/fastText on 37k tokens (minutes), persistent homology on a few thousand points, Gromov–Wasserstein on a few thousand nodes (POT library), spectral decompositions of 8k×8k sparse matrices, and simulation-based inference with small MLP density estimators on low-dimensional summary statistics. A character-level transformer of ~1M parameters (the size used in the forum experiments cited below) trains on 190k characters on two cores in roughly one to three hours per fold.
• Pure-Python packages that install from PyPI (ruptures, hmmlearn, pomegranate, morfessor, gensim, ripser/giotto-tda, POT, sbi, networkx, scikit-learn, PyTorch CPU wheel) are the practical toolkit. If PyPI is also restricted, everything in the top-10 can be written in NumPy/SciPy from scratch except the adaptor-grammar sampler, which is a real effort to reimplement.

Already run by the program (not ranked as untried below): entropy/MI profiles; a 103-language reference distribution; one-to-one and homophonic substitution solvers with planted-key controls and held-out quires; a 2/3-state HMM; BPE merge curves; form–function tests; page-similarity vs physical structure.

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1. Decipherment and unsupervised-translation ML

1.1 Unsupervised cross-lingual embedding alignment and its limits

Citations. Conneau, Lample, Ranzato, Denoyer, Jégou, "Word Translation Without Parallel Data," ICLR 2018, arXiv:1710.04087 (VERIFIED). Søgaard, Ruder, Vulić, "On the Limitations of Unsupervised Bilingual Dictionary Induction," ACL 2018, P18-1072, arXiv:1805.03620 (VERIFIED). Alvarez-Melis & Jaakkola, "Gromov-Wasserstein Alignment of Word Embedding Spaces," EMNLP 2018, D18-1214, arXiv:1809.00013 (VERIFIED).

What it does. Learns monolingual word embeddings for two languages, then finds an orthogonal map (adversarial + Procrustes refinement in MUSE; Gromov–Wasserstein in Alvarez-Melis & Jaakkola) that aligns the two point clouds without any dictionary, under the assumption that the two embedding spaces are approximately isomorphic. Søgaard et al. show the isomorphism assumption fails across typologically distant languages, across domains, and with small corpora; the method degrades to near-zero precision in exactly the regime Voynich occupies (37k tokens, unknown typology, unknown domain match).

Prior application to Voynich/undeciphered scripts. None found in the material for Voynich. The Melbourne MDAP Linear A project (VERIFIED as a project page) announces plans to pre-train on candidate related languages and fine-tune on Linear A; no results or publication listed.

Data requirements. Embeddings for the unknown text (37k tokens is at the very low end; Søgaard reports collapse well above this) and for candidate languages (pretrained fastText vectors, ~1–7 GB per language, a proxy-blocked download; or vectors trained locally from the program's 103-language reference corpora, which would be matched in size and therefore fairer).

Implementation plan. Not recommended as a decipherment tool. If run at all, run it as a calibrated negative: train 100-dimensional word2vec/fastText on the EVA word tokens and on 37k-token excerpts of each reference language; align each reference language to (a) itself with vocabulary relabelled (positive control), (b) a verbose-cipher transform of itself (planted control), (c) Voynich. Report the GW distance or MUSE CSLS precision distribution for (a) and (b) as the detectability floor. The expected finding is that Voynich lies within the noise of (b)-level transforms, which is itself a useful constraint: it bounds how much word-level distributional structure could be recovered by any alignment method at this corpus size. CPU: minutes per language pair with POT's entropic GW on 2–5k vocabulary.

1.2 Neural decipherment (Luo et al.)

Citations. Luo, Cao, Barzilay, "Neural Decipherment via Minimum-Cost Flow: From Ugaritic to Linear B," ACL 2019, P19-1303, arXiv:1906.06718 (VERIFIED). Luo, Hartmann, Santus, Barzilay, Cao, "Deciphering Undersegmented Ancient Scripts Using Phonetic Prior," TACL 2021, 2021.tacl-1.5, arXiv:2010.11054 (VERIFIED).

What it does. Treats decipherment as learning a character-level mapping from a lost script to a known related language, with a neural sequence model constrained by a minimum-cost-flow matching of cognates (2019) and, in 2021, with a phonetic (IPA-feature) prior that lets the model work when word boundaries are unknown and the related language is uncertain. Evaluated on Ugaritic→Hebrew, Linear B→Greek, Gothic, and Iberian; the 2021 paper also uses the method to rank candidate related languages.

Prior application. None found on Voynich in the material. The core assumption, that the plaintext is a known language and the script encodes it phonetically with cognates recoverable, is the same assumption the program's substitution solvers already test with planted keys and held-out quires. Hauer & Kondrak, "Decoding Anagrammed Texts Written in an Unknown Language and Script," TACL 2016, Q16-1006 (VERIFIED) is the closest prior Voynich attempt in this family (language ID over 380 languages plus anagram decoding); its Hebrew result has been widely criticised and is not reproduced here.

Data requirements. Candidate related-language lexicons (IPA transcriptions for the phonetic prior), word-segmented or unsegmented script, and a small GPU in the original work. The 2019 model is a modest LSTM; CPU training is possible but slow (days per candidate language).

Implementation plan. Only worth running as a language-ranking tool, not as a decipherment: for each of a handful of candidate languages (Latin, Italian, German, Hebrew, Arabic, Czech, Occitan), run the 2021 model with the phonetic prior and record the final matching cost; run the same against the planted-key controls the program already has (a known-language text enciphered with a simple substitution and with a Naibbe-style verbose cipher). A positive result would be a candidate language whose cost sits inside the planted-control distribution; the honest prior is that none will. On the 2-core machine this is a 1–2 week background job; it is the only method in this section where CPU time rather than feasibility is the obstacle.

1.3 LLM-based decipherment attempts and evaluations, 2023–2026

Citations. Shih, Lin, Hsieh, "Reasoning Over the Glyphs: Evaluation of LLM's Decipherment of Rare Scripts," arXiv:2501.17785, Jan 2025 (VERIFIED): GPT-4o, Gemini and Claude 3.5 Sonnet on a multimodal puzzle dataset of non-Unicode scripts; results mixed, glyph-to-text description is the bottleneck. Turenne, "A Generative Grammar Underlying the Voynich Manuscript, the Pastiche Hypothesis: Evidence from Large Language Models," arXiv:2609.20835 (VERIFIED; listed submission date 2026-07-28 conflicts with the arXiv id's month — check the PDF): despite the title, LLMs appear only for image-text alignment of plant drawings to Pseudo-Apuleius herbals; the linguistic claims rest on position-dependent probabilistic grammars and are reported as observations with no baselines. Piesiak, Zenodo 10.5281/zenodo.17794596, Dec 2025 (VERIFIED as a record): self-published "99.8% confidence" nomenclator decoding; no stated method for the confidence figure, internally inconsistent dates and counts, unreviewed. Korovina, "A Computational Evaluation of Syllabic Hypotheses for Rongorongo," LT4HALA 2026 (VERIFIED): not an LLM paper, but the best-designed recent evaluation of a decipherment hypothesis on an undeciphered script — a genetic-algorithm search for sign→syllable maps with a fitness function from Rapa Nui n-grams, calibrated on controlled texts (fitness correlates 0.75 with accuracy), a stated noise threshold, and a finding that the real corpus sits at or below that threshold. Tiwari, "Statistical Structure in Indus Sign Sequences," NLP4DH 2026 (VERIFIED): BiLSTM + entropy + KL on 6,579 inscriptions; no stated baselines in the abstract. Corazza et al., "Unsupervised deep learning supports reclassification of Bronze age cypriot writing system," PLOS ONE 2022, PMC9282481 (VERIFIED as listing; content not fetched).

Assessment. No LLM-based Voynich result in the material survives a reading of its own methods section. The two usable lessons come from Korovina (calibrate the fitness function on texts where the answer is known, publish the noise threshold before scoring the real corpus) and from Shih et al. (LLMs cannot even reliably consume non-Unicode glyph sequences). Under the program's constraints (no GPU, no API through the proxy) LLM decipherment is not runnable, and the evidence says it would not be informative if it were.

1.4 Unsupervised machine translation for low-resource and dead languages

Citations. Lample, Conneau, Denoyer, Ranzato, "Unsupervised Machine Translation Using Monolingual Corpora Only," ICLR 2018, arXiv:1711.00043 (VERIFIED as listing). Artetxe et al. 2018 "Unsupervised Neural Machine Translation" (UNVERIFIED).

What it does. Bootstraps a translation model from two monolingual corpora via shared embeddings, denoising auto-encoding and back-translation. It depends on 1.1's alignment step and on corpora of millions of sentences. Søgaard's limits apply with more force. No Voynich application found; none feasible at 37k tokens on CPU. Listed for completeness; not recommended.

1.5 Optimal-transport alignment of word distributions

See 1.1 (Alvarez-Melis & Jaakkola, VERIFIED). The relevant 2022–2024 theory is Ganassali's thesis, "The Graph Alignment Problem: Fundamental Limits and Efficient Algorithms," arXiv:2404.12418 (VERIFIED): for correlated Erdős–Rényi graphs, exact alignment has a sharp threshold at roughly nqs ≈ log n, almost-exact alignment needs nqs → ∞, and partial recovery is impossible when nqs → 0, where s is the edge-correlation between the two graphs. For a Voynich co-occurrence graph aligned to a reference-language graph, s is the unknown quantity of interest; the theory says the program can estimate, from planted controls, the smallest s that would be detectable at n ≈ 2–5k nodes, and report that as the sensitivity of the test. This turns the "it didn't align" result into a quantitative bound. Implementation is in §2.10.

1.6 Transformer language models trained on Voynich

Citations. Two Voynich Ninja forum projects by user quimqu, 2025 (VERIFIED as forum threads 4744 and 4803): GPT-style character-level models (~0.8M parameters) trained from scratch on EVA/Currier subsets with 5-fold cross-validation, validation perplexities ~3.4–4.6, per-folio loss heatmaps, saliency visualisations; no decipherment claim. Community criticism in the thread: no metric showing the model found structure that slot grammars miss; the 96.74% slot-grammar conformity figure is self-validated; the most "anomalous" words are short rare tokens, an artefact of per-token loss. Delétang et al., "Language Modeling Is Compression," ICLR 2024, arXiv:2309.10668 (VERIFIED) is the framing that makes such models useful: a trained LM's held-out cross-entropy is a code length, so LMs of different context lengths give a direct estimate of how much predictability lives at each range.

What is untried. Nobody has reported the context-length scaling curve: held-out bits per glyph as a function of the model's context window (1, 2, 4, 8, 16, 32, 64, 128 glyphs; and the same in word units), on quire-held-out folds, compared with the same curve for (a) reference languages at matched size, (b) the Gaskell–Bowern human-gibberish samples, (c) synthetic text from the autocopy and Naibbe generators. Natural language keeps gaining to long contexts; a self-citation generator should gain only up to the copy window; a verbose cipher of natural language should show the plaintext's gains blurred over a longer range. This is a sharp, pre-registrable discriminator. See top-10 item 2.

1.7 Perplexity-based language identification

Without a mapping from EVA to a phoneme or letter inventory, the perplexity of a reference-language LM on Voynich text is undefined; perplexity-based language ID (as in Hauer & Kondrak 2016, VERIFIED) only works after a candidate substitution is fixed. The program's substitution solvers already do this with planted controls. The one new angle is in 1.6: compare shapes of predictability curves, which need no mapping.

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2. Sequence and statistical methods

2.1 Neural compression and entropy-rate estimation

Citations. Delétang et al. 2024 (VERIFIED, §1.6). Lindemann & Bowern, "Character Entropy in Modern and Historical Texts: Comparison Metrics for an Undeciphered Manuscript," arXiv:2010.14697 (VERIFIED). Gaskell & Bowern, "Gibberish after all? Voynichese is statistically similar to human-produced samples of meaningless text," Voynich 2022 conference, CEUR Vol-3313 paper4 (VERIFIED): 42 metrics including DEFLATE ratio and second-order conditional entropy on 42 volunteers' handwritten gibberish vs 75 meaningful texts; a random forest labelled all Voynich samples as gibberish-like with low confidence; the authors explicitly say higher-level structure was untested. Rozanova & Temerev 2026 (VERIFIED): glyph conditional entropy ~2.7 bits vs ~3.5 for Latin/Italian/English; one token predicts the next by under 1% of token entropy, below every control (2–10%); glyphs at token edges share ~0.2 bits.

What is untried. Entropy-rate estimation beyond order-2 with proper finite-sample correction (Lempel–Ziv estimators, or an LM with growing context as in §1.6) and the excess entropy / predictive information curve (block entropy H(n) minus n·h). Gibberish and self-copy predict a quickly saturating curve; language predicts slow saturation. The Gaskell–Bowern volunteer corpus is the right negative control and was collected for exactly this purpose; whether it is shareable is a question for the authors (a GitHub README for the project is listed, danielgaskell/voynich, VERIFIED as a URL).

Implementation. Block entropies up to n = 8 glyphs directly, with Miller–Madow or NSB bias correction; beyond that, LZ78 code length and the LM curve. Run per section and per scribe, with the same estimators on matched-length reference texts and surrogates. CPU trivial except the LM part (hours).

2.2 Topological data analysis of text

Citations. Zhu, "Persistent Homology: An Introduction and a New Text Representation for Natural Language Processing," IJCAI 2013 (VERIFIED). "Unveiling Topological Structures from Language," arXiv:2411.10298 (VERIFIED as listing; authors not fetched). A 2025-ish "Topological Signature of 19th Century Novelists" item appeared in a listing (VERIFIED as listing only). No Voynich application found; a search for "Voynich" with "persistent homology"/"optimal transport" returned nothing relevant.

What it does. Builds a filtration (Vietoris–Rips) over points — words embedded by co-occurrence, or sliding-window delay vectors of the glyph sequence — and tracks the birth and death of connected components (H0) and loops (H1). Zhu's original construction uses a similarity filtration over sentence/document vectors to capture "tie-backs" (text returning to earlier content).

Assessment. Low prior for a decisive finding, but cheap and never done. The informative version is Zhu's tie-back idea applied at the line/paragraph level: an H1 feature that appears in languages (a paragraph returning to its opening topic) and should be absent in autocopy text, whose similarity structure is a chain with local repetition. Needs a word similarity measure that does not already assume meaning — co-occurrence PPMI vectors or the program's existing page-similarity measure.

Implementation. For each paragraph, build PPMI word vectors from the whole corpus (window 2–5), average to line vectors, take cosine distances between lines within a section, compute persistence diagrams with ripser (a few hundred to a few thousand points; seconds). Compare the H1 total persistence and the number of long bars against (a) reference texts segmented into matched line lengths, (b) line-order permutations within section, (c) generator output. Report Wasserstein distances between diagrams with a permutation p-value. 15–25 h.

2.3 Hyperbolic embeddings

Citation. Nickel & Kiela, "Poincaré Embeddings for Learning Hierarchical Representations," NeurIPS 2017 (UNVERIFIED — not searched). No Voynich application found.

What it does. Embeds a graph or co-occurrence structure in hyperbolic space, where tree-like (hierarchical) structure embeds with low distortion in few dimensions. The diagnostic is the distortion gap: if a 2-D Poincaré embedding of the word co-occurrence graph fits far better than a 2-D Euclidean one, the graph is tree-like. Natural-language co-occurrence graphs are known to be hierarchical (function words as hubs); autocopy text produces a chain-like graph with hubs only from frequency.

Assessment. Secondary. The same question is answered more directly by the spectral and graph measures in §2.9–2.10 (Gromov δ-hyperbolicity is a one-line computation on the shortest-path matrix). Recommended only as that one-line statistic. CPU trivial.

2.4 Information bottleneck

Citation. Tishby, Pereira, Bialek, "The Information Bottleneck Method," 1999 (UNVERIFIED — not searched). Related and more practical: Brown et al. 1992 class-based n-gram clustering (UNVERIFIED). No Voynich application of IB found; Currier's and Stolfi's word classes and the forum HMM (thread 4896, VERIFIED) are hand-built or 2–3-state analogues.

What it does. Compresses words into k classes T that maximise I(T; next word) for a given I(T; word). The result is a set of word classes defined purely by syntactic distribution. In natural language, a few dozen classes capture a large fraction of the adjacent-word MI; the classes alternate in characteristic ways (determiner→noun). Rozanova & Temerev report adjacent-token MI under 1% of token entropy, which predicts that IB classes will capture almost nothing — a testable prediction, and one whose failure would be interesting.

Implementation. Deterministic-annealing IB or agglomerative IB on the 8k×8k bigram count matrix restricted to types with frequency ≥ 3 (~2–3k types); or Brown clustering (exchange algorithm), which is an MI-maximising approximation and runs in minutes on this vocabulary. For k = 2…64, record held-out class-bigram log-likelihood on quire folds; compare with the same procedure on reference languages at 37k tokens, on within-line word-order permutations (destroys syntax, keeps frequencies), and on generator output. Also test whether the induced classes align with word position in line (Feaster's rightwardness, §2.8) or with Zattera's slot grammar — if "syntactic" classes are fully explained by word-form slots, that favours a form-driven generator over a language. 20–30 h.

2.5 Change-point detection for segmentation

Citations. Killick, Fearnhead, Eckley, "Optimal detection of changepoints with a linear computational cost," JASA 2012, arXiv:1101.1438 (VERIFIED). Adams & MacKay, "Bayesian Online Changepoint Detection," arXiv:0710.3742 (VERIFIED). Prior Voynich application: hepialidae, "Illuminating the Illuminated, Part Four: Changepoint Analysis of the Voynich Manuscript," Weird Data Science blog / R-bloggers, Feb 2020 (VERIFIED): a custom Stan multinomial single-changepoint model over per-folio word-length frequencies (2–4-letter words) and 12-topic LDA assignments; found a changepoint near folio 33 (word length) and a diffuse one around folio 38 (topics). Labyrinthinesecurity forum post, 30 Apr 2026 (VERIFIED as thread 5698): unsupervised two-group model on per-page character ratios recovers Currier A/B; 89.2% held-out label prediction; A/B explains ~29% of inter-page variance; data not yet public.

What is untried. Multiple-changepoint detection (PELT allows any number of changes with a penalty chosen by cross-validation or by a known null) on a multivariate per-line feature sequence in physical order (folio, then line), and the comparison of the detected changepoint set with the independently known boundaries: quire breaks, section breaks, scribe changes (Davis 2020, Manuscript Studies 5(1), muse.jhu.edu/article/754633, VERIFIED), Currier A/B, and page turns. The 2020 blog used one changepoint, a per-folio unit, and no comparison to physical structure. The key discriminating prediction: an autocopy process predicts drift (gradual change tracking distance in the text, no sharp changepoints except where the scribe restarts from a new seed); a cipher with periodic key changes predicts sharp changepoints at positions unrelated to layout; a copied natural-language text predicts changepoints at section/topic boundaries. The program's page-similarity-vs-structure result is the static version of this; the sequential version adds the drift-vs-jump distinction.

Implementation. Per line: glyph unigram proportions (reduced to ~15 dimensions by PCA fitted on the whole corpus), mean word length, fraction of words starting with q/o/ch/sh, fraction of line-initial/final markers, Zattera-slot occupancy rates. Run PELT (ruptures, cost = multivariate normal or rank-based) with the penalty swept, and BOCPD with a hazard rate set to 1/(mean section length). Score: for each penalty, precision/recall of detected changepoints against each physical boundary set with a tolerance of ±3 lines; null distribution from circularly shifting the boundary sets (preserves their spacing) and from running PELT on line-order permutations within section. 20–30 h. CPU seconds per run.

2.6 Bayesian nonparametrics for morpheme/word induction

Citations. Johnson, Griffiths, Goldwater, "Adaptor Grammars: A Framework for Specifying Compositional Nonparametric Bayesian Models," NIPS 2006 (VERIFIED; note 2006 proceedings, not 2007). Fox, Sudderth, Jordan, Willsky, "A sticky HDP-HMM with application to speaker diarization," Annals of Applied Statistics 2011, doi:10.1214/10-AOAS395, arXiv:0905.2592 (VERIFIED). Creutz & Lagus, Morfessor (VERIFIED as a listing of a 2006/2007 Helsinki PDF; exact citation UNVERIFIED). Prior Voynich application: none found for adaptor grammars or Morfessor. The forum HMM thread (4896, VERIFIED) uses a hand-built prefix/stem/suffix scorer, not a learned segmentation. The program's own 2/3-state HMM and BPE curves are the closest in-house work.

What it does. An adaptor grammar is a PCFG in which chosen nonterminals (Word, Stem, Suffix, Collocation) are "adapted" by a Pitman–Yor process, so the model caches whole subtrees and learns a lexicon of reusable units at several levels at once, with a principled trade-off between lexicon size and derivation length. It has been the standard for unsupervised word/morpheme segmentation since 2009. An HDP-HMM is an HMM with an unbounded number of states, letting the data choose state count; the "sticky" variant penalises rapid switching.

Why it matters here. The slot-grammar literature (Zattera 2022, VERIFIED, F1 0.270 against 0.081 or lower for other grammars) fits grammars by hand-tuned optimisation and reports F1, which does not compare across model classes. An adaptor grammar yields a held-out marginal likelihood for the same words and a posterior over morph boundaries, so one can ask: does a hierarchical Stem+Suffix(+Prefix) grammar beat a flat 12-slot PCFG on held-out quires? And does the same grammar, fitted to Naibbe-cipher output and to autocopy output of the same size, produce the same lexicon shape (singleton-type fraction, stem count)? Rozanova & Temerev's 70% singleton-type rate vs 41% and 59–60% for the two generator controls is exactly the kind of statistic an adaptor-grammar posterior makes model-based.

Implementation. Mark Johnson's py-cfg C++ sampler (UNVERIFIED availability through the proxy; it is a small source tree on GitHub) or a Python reimplementation of the Pitman–Yor adaptor for a 2–3 level grammar (Word → Prefix? Stem Suffix?; Stem → Glyph+). Input: the ~8k word types with counts, or the 37k tokens, in EVA glyphs and in merged units. 2,000 sweeps on this corpus is hours on one core; run 5 quire folds. HDP-HMM: run pomegranate/own Gibbs sampler over glyph sequences within words to let the data choose between the program's 2/3 states and more; compare held-out likelihood with the fixed-K HMMs. 40–60 h.

2.7 MDL-based grammar induction

Citation. Grünwald, The Minimum Description Length Principle, 2007 (UNVERIFIED). No Voynich application found beyond the F1-based grammar search in Zattera 2022.

What it does. Selects a grammar by total code length (grammar + data given grammar). It is the frequentist twin of §2.6 and gives the same held-out comparison; the practical advantage is that the BPE merge curve the program already has is an MDL-style curve if each merge's saving in code length is recorded. Recommendation: do not run a separate MDL study; instead report the two-part code length at each BPE merge count and at the adaptor-grammar posterior mode, on the same held-out quires, so all word-structure models share one scale (bits per word). 5–10 h on top of §2.6.

2.8 Tests for "is this a language"

Citations. Clauset, Shalizi, Newman, "Power-law distributions in empirical data," SIAM Review 51(4), 2009, arXiv:0706.1062 (VERIFIED). Ferrer-i-Cancho and colleagues: "Dependency distance minimization predicts compression," arXiv:2109.08900 (VERIFIED); "Anti dependency distance minimization in short sequences: a graph theoretic approach," W19-7911 (VERIFIED as listing). Montemurro & Zanette, "Keywords and Co-Occurrence Patterns in the Voynich Manuscript: An Information-Theoretic Analysis," PLOS ONE 2013, PMC3689824 (VERIFIED). Amancio et al., "Probing the statistical properties of unknown texts: application to the Voynich manuscript," PLOS ONE 2013, arXiv:1303.0347 (VERIFIED). Feaster, "Rightward and Downward Grapheme Distributions in the Voynich Manuscript," Voynich 2022, CEUR Vol-3313 paper12 (VERIFIED): a rightwardness/downwardness score per token; minimal pairs differ in position (ch- vs Sh- initial 0.514 vs 0.434; o- vs qo- 0.534 vs 0.468; t vs k 0.523 vs 0.488), persisting mid-line and at glyph level. Bowern & Gaskell, "Enciphered after all? Word-level text metrics are compatible with some types of encipherment," Voynich 2022, CEUR Vol-3313 paper6 (VERIFIED): 22 manipulations × 42 metrics; bigraph encoding, vowel removal, letter sorting and null insertion move Latin toward Voynich values; no single manipulation matches everything. Heaps' law, burstiness (Altmann/Pietronero), Menzerath–Altmann: no specific citations were collected (UNVERIFIED).

Status. Zipf fits, Heaps curves, burstiness and keyword entropy have all been computed on Voynich by several authors (Montemurro & Zanette 2013; Amancio 2013; the 42-metric Yale suite). The weak points in that literature are (i) few used Clauset-style likelihood fitting with a comparison to the lognormal alternative and a goodness-of-fit p-value by semiparametric bootstrap, (ii) nulls were rarely matched to physical structure (page-order permutation vs word-order permutation vs section-preserving permutation), and (iii) Feaster's positional effects were not modelled jointly with word form.

What is untried and worthwhile.

• Heaps/vocabulary-growth under page-order permutation: the vocabulary growth curve in manuscript order vs in 1,000 random page orders vs within-section page orders. A text with topic structure grows vocabulary faster at section boundaries; autocopy with a drifting seed grows it steadily; a nomenclator cipher grows it like its plaintext. Cheap, and a direct test of Montemurro & Zanette's keyword result at the vocabulary level.
• Ferrer-i-Cancho's dependency-length ideas cannot be applied without parses, but one derived prediction can: in natural language the MI between words decays roughly as a power law with distance (Lin & Tegmark 2017, UNVERIFIED), while Markov generators decay exponentially. The program's MI profiles may already contain this; if not, fit both decay forms with the Clauset machinery and report the likelihood ratio, with the Gaskell–Bowern gibberish and the generators as references.
• Positional GLM: regress glyph-class presence on relative line position and line-in-paragraph position with word form as covariate, with a null that permutes word order within lines (keeps line length and composition). This formalises Feaster and tests whether the "line as functional unit" effect is bigger than any reference language's.

10–20 h for all three. CPU trivial.

2.9 Random-matrix and spectral methods on co-occurrence matrices

Citation. Marchenko–Pastur law; application to text co-occurrence: no specific citation collected (UNVERIFIED). No Voynich application found.

What it does. Takes the word×context PPMI or count matrix, computes its singular values, and compares the spectrum to the Marchenko–Pastur bulk expected for a random matrix with the same marginals. The number of singular values above the bulk edge is an estimate of latent dimensionality; the spectral gap pattern distinguishes block structure (topics, word classes) from chain structure.

Why worthwhile. It is a model-free summary that the generators make different predictions about: a language has a handful of large outliers (syntax classes) plus a slowly decaying topical tail; autocopy produces a near-Toeplitz banded structure whose spectrum is close to the bulk; a verbose homophonic cipher spreads each plaintext word over several ciphertext types and therefore lowers the outlier count relative to its plaintext by a predictable factor. It is also the cheapest way to compare Voynich with all 103 reference languages at once.

Implementation. Build the 3k×3k (types with f ≥ 3) PPMI matrix for windows 1, 2 and 5; SVD via scipy.sparse.linalg.svds; null spectra from 200 draws of the configuration-model null (randomly rewire word order preserving unigram counts) and from within-line permutations. Report the count of outliers above the 99th percentile of the null edge, and the effective rank. Run the same on each reference language at 37k tokens, on the gibberish corpus if available, and on each generator. 10–20 h.

2.10 Graph-based methods and network alignment

Citations. Amancio et al. 2013 (VERIFIED) built word co-occurrence networks for Voynich and compared network metrics with reference languages, concluding compatibility with natural language. Ganassali 2022 thesis (VERIFIED, §1.5) for alignment limits. Alvarez-Melis & Jaakkola 2018 (VERIFIED) for the GW algorithm. Network motif analysis and community detection: standard tools, no Voynich-specific citation found beyond Amancio.

What is untried. (a) Motif census and community structure with structure-preserving nulls: Amancio's comparison used global metrics; motif z-scores against degree-preserving rewiring, and modularity against the same, have not been reported for Voynich sections vs scribes vs Currier languages. (b) Alignment: GW alignment of the Voynich co-occurrence graph to each of the 103 reference-language graphs, with the planted-control calibration described in §1.1 and the Ganassali threshold used to convert the result into a bound on the achievable edge-correlation s. The prior is strongly that no language aligns above the planted-control floor; the value is the published floor.

Implementation. networkx for graphs on 2–5k nodes; POT for GW (entropic, ε = 0.01–0.1, a few minutes per pair on CPU); degree-preserving rewiring nulls (200 draws). Alignment score: fraction of top-100 frequency words mapped to a word within rank ±20 of equal frequency is not a good score (frequency alone gives that); use the GW objective value relative to its planted-control distribution. 40–60 h including the control suite.

2.11 Diffusion maps

Citation. Coifman & Lafon 2006 (UNVERIFIED). No Voynich application found.

What it does. Nonlinear embedding of points via the eigenvectors of a diffusion operator on a similarity graph. Applied to pages or lines it recovers a low-dimensional "trajectory" through the manuscript. It overlaps heavily with the program's page-similarity work and with §2.5; the only distinct use is as the feature space fed to PELT/BOCPD (diffusion coordinates of lines instead of raw glyph proportions), where it reduces noise. Not separately ranked. 5 h as a preprocessing option in §2.5.

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3. Rigour tools

3.1 Pre-registration of computational analyses and the garden of forking paths

Citations. Gelman & Loken, "The garden of forking paths," American Scientist 2014 (VERIFIED (partial): the concept and the Gelman blog/Wikipedia entries were seen; the journal citation itself was not). No example of a pre-registered decipherment analysis was found in the material; the closest in spirit is Korovina 2026 (VERIFIED), which fixed a noise threshold on controlled texts before scoring the real corpus.

Practice for this program. A pre-registration document per analysis stating: unitization (EVA glyphs vs merged units); corpus subset (paragraph text only, labels excluded, which transliteration version); the single primary statistic; the null model(s) and the number of surrogate draws; the held-out design (quire folds, with the fold assignment fixed by a published seed); the decision threshold; and what result would count against the hypothesis. Store it with a hash in the repository before running. Every analysis in the top-10 below is written to fit this template.

3.2 Null models and surrogate data

Use a hierarchy of shuffles, each of which destroys one level of structure and keeps everything below it:

1. Glyph permutation within word (keeps word length and glyph inventory; destroys word structure).
2. Word permutation within line (keeps line length and composition; destroys word order and positional effects).
3. Line permutation within page; page permutation within section; section permutation.
4. Markov-chain surrogates: text generated from the fitted order-k glyph or word model, matched in length (keeps k-gram statistics; destroys longer dependence). The program's HMMs and the generators of §4 are higher-order surrogates.
5. Phase randomisation applies to real-valued series only; use it for per-line feature series (e.g. mean word length by line) to test for periodicity vs trend, not for the symbol sequence itself.

Each test should state which level of the hierarchy its null sits at; a result that survives level 2 but not level 3 is a statement about line-internal structure only.

3.3 Multiple-comparison control

Benjamini–Hochberg across families of tests (e.g. 42 metrics × 6 sections) and permutation-based max-statistic control when tests are correlated (compute the maximum statistic over the family in each surrogate draw; compare the observed maximum to that distribution). The 42-metric Yale suite (Gaskell & Bowern 2022, VERIFIED) used Welch bootstrapped t-tests, KDE overlap and a random forest; a reviewer will want the family-wise correction stated.

3.4 Cross-validation across pages and sheets

The program already holds out quires. Two refinements: (i) also hold out by bifolio where the quire structure is uncertain, since a bifolio is the physical unit a scribe wrote across; (ii) stratify folds by scribe and Currier language so that no fold is all-A or all-scribe-2, otherwise a key or model fitted on A will appear to fail on B for reasons of dialect rather than overfitting. Report both pooled and per-stratum held-out scores.

3.5 Bayes factors, held-out likelihood, posterior predictive checks

For competing generative models (§4), the held-out log-likelihood on quire folds is the primary comparison; it needs no prior on model class and is what a sceptic will accept. Bayes factors are appropriate only between models with proper likelihoods and well-specified priors (n-gram, HMM, PCFG, adaptor grammar); the autocopy and Naibbe generators have no tractable likelihood and are compared by likelihood-free methods (§4.5). Posterior predictive checks: for each fitted model, simulate 200 corpora of the same size and layout, compute the same summary statistics as for the real text (the 42-metric suite plus the new ones here), and report which statistics the real text falls outside the 95% predictive interval for. This is the single most informative table the program can produce: a model × statistic grid of where each generator fails.

3.6 Simulation-based calibration

Citation. Talts, Betancourt, Simpson, Vehtari, Gelman, "Validating Bayesian Inference Algorithms with Simulation-Based Calibration," arXiv:1804.06788 (VERIFIED). The sbi package documents an SBC how-to (VERIFIED as listing).

Use. Before trusting a posterior over generator parameters (e.g. the autocopy copy-window distribution, or the Naibbe table size), draw parameters from the prior, simulate a corpus, infer, and check that the rank of the true parameter among posterior draws is uniform. This catches a mis-specified inference pipeline before it is applied to the real text. 10–15 h per model, included in §4 estimates.

3.7 Examples of statistical validation of solutions

• Zodiac-340. Oranchak, Van Eycke and Blake, December 2020 (solution; the HistoCrypt paper from the solvers is VERIFIED as a PDF listing at ecp.ep.liu.se/histocrypt/395 but was not fetched). von zur Gathen, "Unicity distance of the Zodiac-340 cipher," Cryptology ePrint 2021/1620 (VERIFIED): key entropy ≈ 562.6 bits; plaintext entropy 1.8 bits/char from a 14,825-character Zodiac corpus; unicity distance 80–152 characters, below the 340-character length; robustness check at entropies 1.36 and 2.30 (132 and 183). The validation is a unicity argument, not a null test, and the author leaves open whether other solutions exist. Lesson for Voynich: a unicity calculation for any proposed cipher class is cheap and should accompany every proposal; for a verbose homophonic cipher with a large table the key entropy is high enough that the unicity distance may exceed the corpus, which is itself a result (the cipher class would be unfalsifiable from the text alone).
• Copiale. Knight, Megyesi, Schaefer, "The Copiale Cipher," ACL 2011 Workshop on Building and Using Comparable Corpora, W11-1202 (VERIFIED). The validation was readability of the German plaintext plus consistency across the whole document; no formal null. The Voynich analogue is the planted-key control the program already uses.
• Book of Soyga. Reeds, "John Dee and the Magic Tables in the Book of Soyga" (VERIFIED as an archive.org PDF and a Wikipedia entry; the printed citation — in Clucas (ed.), John Dee: Interdisciplinary Studies, 2006 — is UNVERIFIED). The tables were shown to be generated by a simple recurrence; the validation is exact reproduction of 36 tables from a short rule. The lesson is the standard: a generating algorithm is established when it reproduces the artefact exactly, not when it matches its statistics. None of the Voynich generators (§4) meets that bar, and the comparison should say so.

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4. Generative-model fitting

4.1 Timm & Schinner self-citation (autocopy)

Citations. Timm & Schinner, "A possible generating algorithm of the Voynich manuscript," Cryptologia 2020 (VERIFIED (partial): title/journal/year seen on the author's Academia page and in forum threads; volume 44(1) and DOI not confirmed in any fetched page). Timm & Schinner, "The Voynich manuscript: discussion of text creation hypotheses," Cryptologia 2024 (VERIFIED (partial), same source). Timm, "The Challenge of Analyzing a Dynamic Text," Cryptologia 2026 (VERIFIED (partial)). Timm, "How the Voynich Manuscript was created," arXiv:1407.6639 (VERIFIED as listing). Forum criticism (Emma May Smith, thread 2790, VERIFIED): the paper's Figure 4 (edit distance vs textual distance) was compared against Alice in Wonderland, a topically uniform text; herbals would be the fair control.

What it does. Each new word is a modified copy of a word visible earlier on the page (or nearby), via a small set of glyph edits; the process reproduces low entropy, local repetition, Zipf-like frequencies and the A/B drift.

Fitting. Likelihood is intractable (the copy source and edit path are latent), but the generator is cheap to simulate. Parameters: copy-distance distribution, edit-type probabilities, seed set per page, restart probability. Fit by simulation-based inference (§4.5) on summary statistics: edit-distance-vs-distance curve (Timm's Figure 4 statistic, computed against herbal controls as Smith suggests), the §2.5 drift signature, singleton-type fraction, adjacent-token MI, and the Feaster positional statistics (Feaster argues the current model does not account for them; the fit will say whether any parameter setting can).

4.2 Rugg's table-and-grille

Citation. Rugg, "An Elegant Hoax? A Possible Solution to the Voynich Manuscript," Cryptologia 28(1), 2004 (VERIFIED via the Stolfi bibliography entry; pages not listed). Critiques: Schmeh, Klausis Krypto Kolumne, 2016, two parts (VERIFIED as listings).

What it does. A table of syllable fragments (prefix/mid/suffix columns) read through a card with cut-out windows, moved across the table; produces slot-structured words with repetition patterns from the grille movement.

Fitting. Parameters: table dimensions, column contents (fit from the slot grammar), grille geometry, movement rule. Simulation only. The sharpest prediction is periodicity: a grille moving regularly produces word-feature autocorrelation at lags equal to the grille's step pattern; test with the spectrum of the per-word slot-occupancy series (phase-randomisation null applies here). A null spectrum for Voynich at all plausible lags is strong evidence against the fixed-grille variant.

4.3 Greshko's Naibbe cipher

Citation. Greshko, "The Naibbe cipher: a substitution cipher that encrypts Latin and Italian as Voynich Manuscript-like ciphertext," Cryptologia, online 26 Nov 2025, doi:10.1080/01611194.2025.2566408 (VERIFIED via sci.news summary; the statistical evaluation section was not fetched and the summary says the article does not detail the metrics). A verbose homophonic substitution: each plaintext letter maps to several glyph strings, chosen with playing cards (78-card tarocchi or 52-card variants), output constrained to an expanded slot grammar; replication of Currier B is reported as incomplete.

Fitting. The cipher has a tractable likelihood given the table (a hidden-semi-Markov decoding of plaintext letters from glyph strings), so a proper held-out likelihood is possible: fit the table on training quires by EM over plaintext-language n-grams for each candidate plaintext language, score held-out quires. Compare with the same procedure on the planted controls the program already has (known Latin enciphered with a Naibbe-style table). The program's homophonic solver is the one-glyph-per-letter special case; the verbose case is the gap. Simulation for the summary-statistic route is also straightforward.

4.4 HMM and PCFG

The program's 2/3-state HMM and BPE curves exist. The additions: (i) an HDP-HMM to let the data pick K (§2.6); (ii) a word-level PCFG from Zattera's slot grammar converted to a probabilistic grammar with maximum-likelihood rule weights (so it has a held-out likelihood rather than an F1); (iii) the adaptor grammar (§2.6). All three have proper likelihoods and can be compared by held-out bits per word on quire folds and by posterior predictive checks.

4.5 Simulation-based inference and ABC

Citation. Cranmer, Brehmer, Louppe, "The frontier of simulation-based inference," PNAS 2020, arXiv:1911.01429, PMC7720103 (VERIFIED). sbi package (VERIFIED as a docs listing).

What it does. Replaces the likelihood with a learned density (neural posterior estimation) or with rejection on summary-statistic distance (ABC). Neural posterior estimation with a small masked autoregressive flow on 20–40 summary statistics trains on CPU in under an hour with 10–50k simulations; the simulators here (autocopy, Naibbe, grille) each generate a 37k-word corpus in seconds in NumPy, so 50k simulations is hours per model.

Protocol. For each generator: define the prior over parameters, simulate, train NPE, run SBC (§3.6), then infer the posterior from the real text's statistics. Then the decisive step: posterior predictive checks on held-out statistics not used in training (e.g. train on entropy/Zipf/MI statistics, check on the §2.5 drift signature, the Feaster positional statistics, the §2.9 spectrum). A model whose posterior predictive interval misses held-out statistics is rejected on evidence it was not fitted to. Model comparison among simulators is by the ABC evidence approximation or by a classifier-based test (train a classifier to distinguish simulator outputs; see where the real text lands with calibrated probabilities, and report the classifier's accuracy on held-out simulations as its reliability). 80–120 h for the full suite across four generators plus the LM baselines; this is the largest single item and the one most likely to yield a result a sceptic will accept.

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5. Computer vision, 2022–2026

5.1 HTR on unknown scripts

Citations. Kiessling, "Kraken — an Universal Text Recognizer for the Humanities," DH2019 abstract (VERIFIED at dh-abstracts.library.virginia.edu/works/9912; kraken.re docs VERIFIED). Li et al., "TrOCR: Transformer-Based Optical Character Recognition with Pre-Trained Models," AAAI 2023 (VERIFIED as listing). "A tailored Handwritten-Text-Recognition System for Medieval Latin," arXiv:2308.09368 (VERIFIED as listing). Transkribus: a cloud service; not reachable from a restricted environment (UNVERIFIED citation; not needed).

Prior Voynich application. Bernasconi & Ferilli, IRCDL 2024, CEUR Vol-3643 paper10 (VERIFIED) and the expanded version in Information 16(2):119, 2025, doi:10.3390/info16020119 (VERIFIED): Canny/contour segmentation of ~10 page images → 6,383 symbols → K-means/agglomerative clustering with Otsu + PCA → 26 clusters → CNN classifier; no Voynich accuracy figure in the body text, uneven class distribution, clusters "need validation by humanists." Davis 2020 (VERIFIED) is the palaeographic baseline: five scribes, with a glyph inventory argued from letterforms. Farrugia, Layfield, van der Plas, Voynich 2022, CEUR Vol-3313 paper5 (VERIFIED): character n-gram classifiers recover Davis's scribes 1–3 at 84–90% (10-fold CV), scribes 2 and 3 confused.

What is untried and feasible. The EVA transliteration is line-aligned to the images, so it is a training label set for a line-level HTR model, which no prior work has used. Training Kraken's CRNN on ~5,000 lines on CPU is slow (days) but possible; the payoff is not transcription (already have it) but the alignment the CTC decoder produces: per-glyph bounding boxes across the whole manuscript. With boxes, three things become measurable at scale that Rozanova & Temerev did for a sample: space widths at confident vs uncertain separators, glyph-shape variance within an EVA class across scribes (does EVA's "ch" cover two shapes?), and ligature frequency by position. The alternative without any neural model is the Bernasconi pipeline (connected components + classical features + clustering) with HOG or Zernike moment features and HDBSCAN, which runs on CPU in hours and yields an independent glyph inventory to compare with EVA's. Both are controlled by a positive control on a known-script manuscript page set with the same pipeline.

5.2 Unsupervised glyph clustering and segmentation with foundation models

Citations. Kirillov et al., "Segment Anything," ICCV 2023 (VERIFIED). DINOv2 (Oquab et al. 2023, UNVERIFIED). CLIP (Radford et al. 2021, UNVERIFIED).

Feasibility. SAM ViT-B weights are ~375 MB, DINOv2 ViT-S ~85 MB, CLIP ViT-B/32 ~350 MB; CPU inference on 500 figures and ~230 pages is hours, acceptable. The blocker is the download. If one of these can be fetched once, DINOv2 patch features on glyph crops give a much better clustering than HOG for §5.1, and SAM gives figure/text masks for layout. Mark all three as conditional.

5.3 Layout analysis and diagram parsing

Citation. LayoutLM (Xu et al. 2020, UNVERIFIED) and successors need pretrained weights and a text channel that assumes a readable script; not applicable. Classical layout (text-line detection by projection profiles, figure masks by colour/texture) is sufficient for the program's layout needs and runs on CPU. Diagram parsing (the circular astronomical and cosmological diagrams) is a bespoke geometry task: polar unwrapping of the circular diagrams followed by the same line-level pipeline, so that ring text becomes lines and ring-position becomes a positional covariate for §2.8. 20–30 h, no pretrained model.

5.4 Vision-language retrieval over manuscript collections

Citations. Evron, Bar-Asher Siegal, Fire, "Studying Illustrations in Manuscripts: An Efficient Deep-Learning Approach," arXiv:2601.05269 (VERIFIED): a detect→extract→embed pipeline for illuminated manuscripts (Vatican Library, Bible of Borso d'Este); vision-language embedding for search and clustering; no quantitative metrics in the fetched content. "Multimodal Search on Iconclass using Vision-Language Pre-Trained Models," arXiv:2306.16529 (VERIFIED as listing; authors not confirmed). Turenne 2026 (VERIFIED) used LLM image-text alignment to match Voynich plants to Pseudo-Apuleius herbals, with no reported baseline.

Assessment. The scientifically interesting version is retrieval of Voynich plant and diagram drawings against IIIF-served herbals with a control: retrieval precision of a known herbal's drawings against the same corpus, so that a "match" for Voynich can be scored relative to what the method does for a manuscript whose exemplar is known. This needs CLIP or similar (download) and access to IIIF endpoints through the proxy; both are uncertain. Not ranked in the top-10 on feasibility grounds, but it is the one CV item that could produce a historical rather than a statistical finding, and should be scheduled if the weight download succeeds.

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6. Feasibility summary on the program's machine

| Method | CPU 2-core | GPU needed | Pretrained download needed | Notes | |---|---|---|---|---| | SBI/ABC generator fitting (§4.5) | Yes (hours–days) | No | No | NumPy simulators + small flows | | LM context-scaling curve (§1.6/2.1) | Yes (1–3 h/fold) | No | No | ~1M-param char transformer; n-gram baseline instant | | PELT/BOCPD (§2.5) | Yes (seconds) | No | No | ruptures or own | | Adaptor grammar / HDP-HMM (§2.6) | Yes (hours) | No | No | sampler source needed or reimplement | | IB / Brown clustering (§2.4) | Yes (minutes) | No | No | | | GW graph alignment (§2.10) | Yes (minutes/pair) | No | No (train vectors locally) | pretrained fastText not needed | | Spectral/RMT (§2.9) | Yes (seconds) | No | No | | | Heaps/burstiness/positional GLM (§2.8) | Yes | No | No | | | Persistent homology (§2.2) | Yes (seconds–minutes) | No | No | ripser | | Classical glyph segmentation + clustering (§5.1) | Yes (hours) | No | No | HOG/Zernike + HDBSCAN | | Kraken HTR training on EVA lines (§5.1) | Marginal (days) | Preferred | No (train from scratch) | | | DINOv2/SAM/CLIP features (§5.2, 5.4) | Inference yes (hours) | Preferred | Yes (85 MB–2.5 GB) | blocked unless proxy allows | | Luo neural decipherment (§1.2) | Marginal (weeks) | Preferred | No | low expected value | | MUSE with pretrained vectors (§1.1) | Yes | No | Yes (GB per language) | use locally trained vectors instead | | LLM decipherment (§1.3) | No | Yes / API | Yes | not runnable; evidence says not informative | | Transkribus (§5.1) | No (cloud) | — | — | unreachable |

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7. Ranked top-10 untried techniques

Each item gives the hypothesis, the pre-registered prediction, the null, the control, and an effort estimate (hours of one person's work, including writing the pre-registration and the controls; compute time excluded where it is background).

1. Held-out generator competition with simulation-based inference and posterior predictive checks (§4, §3.5–3.6). This is the only item that addresses the central question directly — which class of process produced the text — in a way that a sceptic can audit. Four simulators (autocopy, Naibbe-class verbose cipher, Rugg grille, slot-PCFG) and two likelihood models (n-gram and adaptor grammar) are fitted on training quires; the autocopy, cipher and grille models by neural posterior estimation on 20–40 summary statistics, the others by maximum likelihood. Each fitted model then simulates 200 corpora with the real page/line layout and is scored on a second, disjoint set of statistics it was not fitted to. The product is a model × statistic grid of 95% predictive-interval misses. Hypothesis: at least one generator class is consistent with all held-out statistics. Prediction (pre-registered): the autocopy model will fail the Feaster positional statistics and the edge-glyph coupling; the Naibbe-class cipher will fail the singleton-type fraction and the Currier B statistics (Greshko reports incomplete B replication); the natural-language-plus-cipher models will fail the adjacent-token MI floor. Null: for each statistic, the model's own predictive distribution. Control: simulation-based calibration of every inference pipeline before touching the real text; a planted run where the "real text" is a simulator's output with known parameters, which must be recovered. Effort: 80–120 h.

2. Context-length scaling of held-out predictability (§1.6, §2.1). Train order-k glyph n-grams (k = 1…8, Kneser–Ney) and a ~1M-parameter character transformer with context windows 16, 32, 64, 128 on quire-held-out folds; record bits per glyph as a function of context. Repeat in word units. Hypothesis: Voynichese carries predictive information beyond the word (i.e. beyond ~8 glyphs). Prediction: if the text is a self-copy process, the curve flattens at the copy window (tens of glyphs) and the gain beyond 32 glyphs is within the gibberish controls' range; if natural language under a cipher, gains persist to 64–128 glyphs at a rate comparable to the reference languages at 37k tokens after the same cipher transform. Null: within-line word-order permutation (removes beyond-word dependence while keeping word structure) and line-order permutation within page. Control: the same curves on 103 reference languages truncated to 37k tokens, on the Gaskell–Bowern gibberish if obtainable, and on each §4 simulator's output. Effort: 25–40 h plus ~30 h CPU background.

3. Multiple-changepoint detection on the line sequence in physical order (§2.5). PELT and BOCPD on per-line feature vectors, scored against quire, section, scribe, Currier and page boundaries. Hypothesis: changes in the text's statistics are located at physical/structural boundaries rather than being gradual or arbitrary. Prediction: a copied natural-language text gives changepoints concentrated at section boundaries with precision above the circular-shift null; an autocopy process gives few changepoints and a monotone drift statistic (autocorrelation of line features decaying with line distance within section, not resetting at page turns); a periodically re-keyed cipher gives changepoints at regular intervals unrelated to layout. Null: circular shifts of the boundary sets (preserves spacing) for the precision/recall statistic; line-order permutation within section for the changepoint count. Control: the same pipeline on a reference-language herbal split into matched pages/lines, and on simulator outputs with the real layout. Effort: 20–30 h.

4. Adaptor-grammar word-structure induction compared with the slot grammar by held-out likelihood (§2.6–2.7). Fit a Pitman–Yor adaptor grammar (Word → Prefix? Stem Suffix?) and a probabilistic version of Zattera's 12-slot grammar; compare on held-out quires in bits per word, alongside the BPE code-length curve. Hypothesis: Voynich words have hierarchical, reusable sub-word units (morphology-like) rather than a flat positional template. Prediction: if hierarchical, the adaptor grammar beats the slot PCFG by more than it does on the Naibbe-cipher control (where structure is a flat table) and the posterior stem lexicon is small relative to the type count; if flat, the slot PCFG wins or ties. Null: glyph permutation within word (destroys all internal structure; sets the floor), and the same models on word lists sampled from the slot PCFG itself. Control: reference languages' word lists at 8k types (where Stem+Suffix should win clearly) and simulator outputs. Effort: 40–60 h.

5. Word-class induction by information bottleneck / Brown clustering with held-out predictive gain (§2.4). Hypothesis: there exist word classes, defined only by context, that carry syntax-like information. Prediction: if the text has syntax, held-out class-bigram log-likelihood for k = 16–64 classes exceeds the within-line-permutation null by an amount comparable to reference languages at 37k tokens (where it is large) rather than to gibberish (near zero); the induced classes will not be fully explained by Zattera slot membership or by line position. Null: within-line word permutation. Control: reference languages, simulators; a second control where the classes are induced on training quires and the gain is measured on held-out quires to rule out memorisation. Effort: 20–30 h.

6. Gromov–Wasserstein alignment of the co-occurrence graph against the 103 reference languages with planted calibration (§1.5, §2.10). Hypothesis: the Voynich word co-occurrence graph is structurally isomorphic, above the detectability floor, to some reference language's graph. Prediction (pre-registered as the likely outcome): no reference language's GW objective falls below the 5th percentile of the planted-control distribution; the result is reported as an upper bound on the edge correlation s with any tested language, using Ganassali's threshold. Null: alignment of each reference language to a different reference language of matched size. Control (positive): each reference language aligned to a relabelled copy of itself and to a verbose-cipher copy of itself (must align); if the cipher copy does not align, the method cannot in principle find a cipher-transformed language, and that is the published finding. Effort: 40–60 h.

7. Spectral and random-matrix analysis of co-occurrence matrices (§2.9). Hypothesis: the latent dimensionality (number of singular values above the Marchenko–Pastur edge of a marginal-preserving null) of Voynich co-occurrence is in the natural-language range. Prediction: languages at 37k tokens show a specific outlier count distribution (to be measured first, on the 103 references); autocopy output shows fewer outliers; verbose ciphers show the plaintext's count reduced by a factor near the mean homophone multiplicity. The Voynich count, by section, is then placed against these. Null: configuration-model rewiring (preserves unigram counts). Control: references and simulators as above. Effort: 10–20 h.

8. Glyph-inventory audit from images, aligned to EVA lines (§5.1). Classical segmentation (connected components, with a merge step for touching strokes) and HOG/Zernike features clustered with HDBSCAN on all paragraph lines; if the DINOv2 download succeeds, replace features. Hypothesis: EVA's glyph inventory matches the shape clusters in the images one-to-one. Prediction: clusters will split some EVA classes by scribe (expected; nuisance) but, under the "glyph is not a letter" result, will also merge frequent EVA bigrams into single shape units at rates above the positive control. Null: cluster/EVA agreement when EVA labels are permuted within line. Control (positive): the same pipeline on a Latin manuscript with a known transcription, which sets the expected agreement for a correct inventory. Also delivers space-width measurements at confident vs uncertain separators across the whole manuscript. Effort: 60–100 h; marginal on CPU for the neural variant.

9. Vocabulary growth, burstiness and positional GLM under layout-preserving nulls (§2.8). Three cheap, pre-registrable tests on structure the existing literature measured with the wrong null. Hypothesis: vocabulary growth and glyph position depend on the manuscript's physical order and layout in the way a topically organised natural-language text does. Prediction: Heaps curve in manuscript order lies outside the page-permutation envelope (topic structure) but inside the section-preserving envelope; Feaster's positional effects, modelled with word form as covariate, exceed the largest effect in any reference language (which would favour a line-driven generator) or do not (which would favour a copied text with line-initial conventions). Null: page-order permutation; within-line word permutation. Control: references and simulators. Effort: 10–20 h.

10. Persistent homology of line-similarity structure within sections (§2.2). Hypothesis: paragraphs show topical "return" structure (H1 loops in Zhu's sense) absent from self-copy text. Prediction: total H1 persistence of Voynich sections lies with references rather than with autocopy output; line-order permutation within section removes it. Null: line permutation. Control: references and simulators. Low prior, but cheap and never done; placed last because its interpretation depends on a similarity measure that items 5 and 7 will have validated first. Effort: 15–25 h.

Not ranked, with reasons: LLM decipherment (not runnable; evidence says uninformative); Luo neural decipherment (its assumptions are those of the program's substitution solvers, already tested with planted keys; CPU cost weeks); MUSE-style embedding alignment (dominated by item 6); diffusion maps and hyperbolic embeddings (subsumed as preprocessing/one-line statistics in items 3 and 7); Transkribus (unreachable); CLIP/IIIF iconographic retrieval (potentially the most historically valuable item, but blocked on weight download and IIIF access; schedule if either clears).

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8. Evaluation protocol a sceptical reviewer would accept

1. Unit of analysis declared. Every analysis runs twice: EVA glyphs and merged units (BPE at the program's chosen merge count). Paragraph text only unless the hypothesis concerns labels. Transliteration version and the handling of uncertain spaces (as spaces; as non-spaces; dropped lines) stated.
2. Pre-registration. One document per analysis, hashed and stored before the run, stating the primary statistic, the prediction under each live hypothesis (language-under-cipher, self-copy, table/grille, meaningless-by-hand), the null level from the §3.2 hierarchy, the number of surrogate draws (≥ 1,000 for permutation p-values; ≥ 200 for posterior predictive checks), the held-out design, and the decision rule.
3. Held-out design. Five quire folds, fold assignment fixed by a published seed, stratified so each fold contains both Currier languages and at least two scribes. Report pooled and per-stratum results. Anything with tunable hyperparameters (penalties, k, context length) is tuned on training folds only.
4. Controls, always three. (a) Reference languages at 37k tokens from the program's 103-language set, with and without the cipher transforms of Bowern & Gaskell 2022; (b) generator outputs from §4 with the real layout; (c) human gibberish (Gaskell & Bowern 2022) if obtainable, else noted as a missing control. A positive control in which the method is shown to detect the effect on a text where it is known to exist is required before the Voynich result is reported.
5. Multiple comparisons. Benjamini–Hochberg within each pre-registered family at q = 0.05; max-statistic permutation control where statistics are correlated. Exploratory analyses are labelled as such and carry no p-values.
6. Decision thresholds. A result counts against a generator class when the real text falls outside that class's 95% posterior predictive interval on ≥ 2 pre-registered held-out statistics after SBC has passed. A result counts for "beyond-word structure" (items 2, 5, 10) when the held-out gain exceeds the 95th percentile of the within-line permutation null and exceeds the median of the gibberish/autocopy controls. A negative alignment (item 6) is reported with its detectability bound, not as "no language."
7. Reporting. For each item: the model × statistic grid (which models fail which statistics), effect sizes with permutation confidence intervals, the fold-wise results, the control results in the same table, and the pre-registration hash. Code and surrogate seeds published. No result is described as a decipherment; the strongest available claim from any of these methods is a ranking of generator classes by their failure to predict held-out structure.

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9. Reference list with verification status

• Adams, R. P., & MacKay, D. J. C. (2007). Bayesian Online Changepoint Detection. arXiv:0710.3742. VERIFIED
• Alvarez-Melis, D., & Jaakkola, T. (2018). Gromov-Wasserstein Alignment of Word Embedding Spaces. EMNLP, D18-1214; arXiv:1809.00013. VERIFIED
• Amancio, D. R., et al. (2013). Probing the statistical properties of unknown texts: application to the Voynich Manuscript. PLOS ONE; arXiv:1303.0347; PMC3699599. VERIFIED
• Artetxe, M., et al. (2018). Unsupervised Neural Machine Translation. ICLR. UNVERIFIED
• Bernasconi, E., & Ferilli, S. (2024). A tool for empowering Symbol Detection through Technological Integration in Library Science. A case study on the Voynich manuscript. IRCDL 2024, CEUR Vol-3643, paper10. VERIFIED
• Bernasconi, E., & Ferilli, S. (2025). Enhancing Symbol Recognition in Library Science via Advanced Technological Solutions. Information 16(2):119. doi:10.3390/info16020119. VERIFIED
• Bowern, C., & Gaskell, D. E. (2022). Enciphered after all? Word-level text metrics are compatible with some types of encipherment. Voynich 2022, CEUR Vol-3313, paper6. VERIFIED
• Bowern, C., & Lindemann, L. (2021). The Linguistics of the Voynich Manuscript. Annual Review of Linguistics (PDF at alumniacademy.yale.edu; lingbuzz/005939 is a review of it by Timm). VERIFIED (partial: volume/pages not seen)
• Brown, P. F., et al. (1992). Class-based n-gram models of natural language. Computational Linguistics. UNVERIFIED
• Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Review 51(4). arXiv:0706.1062. VERIFIED
• Coifman, R., & Lafon, S. (2006). Diffusion maps. Applied and Computational Harmonic Analysis. UNVERIFIED
• Conneau, A., Lample, G., et al. (2018). Word Translation Without Parallel Data. ICLR; arXiv:1710.04087. VERIFIED
• Corazza, M., et al. (2022). Unsupervised deep learning supports reclassification of Bronze age cypriot writing system. PLOS ONE; PMC9282481. VERIFIED (listing; content not fetched)
• Cranmer, K., Brehmer, J., & Louppe, G. (2020). The frontier of simulation-based inference. PNAS; arXiv:1911.01429; PMC7720103. VERIFIED
• Creutz, M., & Lagus, K. Morfessor (Helsinki PDF listed). VERIFIED (partial: exact citation not seen)
• Davis, L. F. (2020). How Many Glyphs and How Many Scribes? Digital Paleography and the Voynich Manuscript. Manuscript Studies 5(1). muse.jhu.edu/article/754633. VERIFIED
• Delétang, G., et al. (2024). Language Modeling Is Compression. ICLR; arXiv:2309.10668. VERIFIED
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• Farrugia, K., Layfield, C., & van der Plas, L. (2022). Demystifying the scribes behind the Voynich Manuscript using Computational Linguistic Techniques. Voynich 2022, CEUR Vol-3313, paper5. VERIFIED
• Feaster, P. (2022). Rightward and Downward Grapheme Distributions in the Voynich Manuscript. Voynich 2022, CEUR Vol-3313, paper12. VERIFIED
• Ferrer-i-Cancho, R., et al. Dependency distance minimization predicts compression. arXiv:2109.08900. VERIFIED
• Ferrer-i-Cancho, R., et al. (2019). Anti dependency distance minimization in short sequences: a graph theoretic approach. W19-7911. VERIFIED (listing)
• Fox, E. B., Sudderth, E. B., Jordan, M. I., & Willsky, A. S. (2011). A sticky HDP-HMM with application to speaker diarization. Annals of Applied Statistics. doi:10.1214/10-AOAS395; arXiv:0905.2592. VERIFIED
• Ganassali, L. (2022). The Graph Alignment Problem: Fundamental Limits and Efficient Algorithms. PhD thesis; arXiv:2404.12418. VERIFIED
• Gaskell, D. E., & Bowern, C. (2022). Gibberish after all? Voynichese is statistically similar to human-produced samples of meaningless text. Voynich 2022, CEUR Vol-3313, paper4. VERIFIED
• Gelman, A., & Loken, E. (2014). The garden of forking paths. American Scientist. VERIFIED (partial: concept/blog/Wikipedia seen; journal page not)
• Greshko, M. A. (2025). The Naibbe cipher: a substitution cipher that encrypts Latin and Italian as Voynich Manuscript-like ciphertext. Cryptologia, online 26 Nov 2025. doi:10.1080/01611194.2025.2566408. VERIFIED (via sci.news summary)
• Grünwald, P. (2007). The Minimum Description Length Principle. MIT Press. UNVERIFIED
• Hauer, B., & Kondrak, G. (2016). Decoding Anagrammed Texts Written in an Unknown Language and Script. TACL, Q16-1006. VERIFIED
• hepialidae (2020). Illuminating the Illuminated, Part Four: Tempora Mutantur — Changepoint Analysis of the Voynich Manuscript. Weird Data Science / R-bloggers, Feb 2020. VERIFIED
• Johnson, M., Griffiths, T. L., & Goldwater, S. (2006). Adaptor Grammars: A Framework for Specifying Compositional Nonparametric Bayesian Models. NIPS 19. VERIFIED
• Kiessling, B. (2019). Kraken — an Universal Text Recognizer for the Humanities. DH2019; kraken.re. VERIFIED
• Killick, R., Fearnhead, P., & Eckley, I. A. (2012). Optimal detection of changepoints with a linear computational cost. JASA; arXiv:1101.1438. VERIFIED
• Kirillov, A., et al. (2023). Segment Anything. ICCV 2023. VERIFIED
• Knight, K., Megyesi, B., & Schaefer, C. (2011). The Copiale Cipher. ACL BUCC workshop, W11-1202. VERIFIED
• Korovina, E. (2026). A Computational Evaluation of Syllabic Hypotheses for Rongorongo: Evidence from N-gram Analysis. LT4HALA 2026 @ LREC, pp. 177–183. VERIFIED
• Labyrinthinesecurity (2026). Generative and Predictive Modeling Confirms Currier's A/B Distinction. Voynich Ninja thread 5698, 30 Apr 2026. VERIFIED (forum post; data not public)
• Lample, G., et al. (2018). Unsupervised Machine Translation Using Monolingual Corpora Only. ICLR; arXiv:1711.00043. VERIFIED (listing)
• Li, M., et al. (2023). TrOCR: Transformer-Based Optical Character Recognition with Pre-Trained Models. AAAI 2023. VERIFIED (listing)
• Lin, H. W., & Tegmark, M. (2017). Critical behavior in physics and probabilistic formal languages. Entropy. UNVERIFIED
• Lindemann, L., & Bowern, C. (2020). Character Entropy in Modern and Historical Texts: Comparison Metrics for an Undeciphered Manuscript. arXiv:2010.14697. VERIFIED
• Luo, J., Cao, Y., & Barzilay, R. (2019). Neural Decipherment via Minimum-Cost Flow: From Ugaritic to Linear B. ACL, P19-1303; arXiv:1906.06718. VERIFIED
• Luo, J., Hartmann, F., Santus, E., Barzilay, R., & Cao, Y. (2021). Deciphering Undersegmented Ancient Scripts Using Phonetic Prior. TACL, 2021.tacl-1.5; arXiv:2010.11054. VERIFIED
• Montemurro, M. A., & Zanette, D. H. (2013). Keywords and Co-Occurrence Patterns in the Voynich Manuscript: An Information-Theoretic Analysis. PLOS ONE; PMC3689824. VERIFIED
• Multimodal Search on Iconclass using Vision-Language Pre-Trained Models. arXiv:2306.16529. VERIFIED (listing; authors not confirmed)
• Nickel, M., & Kiela, D. (2017). Poincaré Embeddings for Learning Hierarchical Representations. NeurIPS. UNVERIFIED
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• Shih, Y.-F., Lin, Z.-L., & Hsieh, S.-K. (2025). Reasoning Over the Glyphs: Evaluation of LLM's Decipherment of Rare Scripts. arXiv:2501.17785. VERIFIED
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• Sterneck, R., Polish, A., & Bowern, C. (2021). Topic Modeling in the Voynich Manuscript. arXiv:2107.02858. VERIFIED
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• Zhu, X. (2013). Persistent Homology: An Introduction and a New Text Representation for Natural Language Processing. IJCAI 2013. VERIFIED