Survey: inductive methods from fourteen fields
Inductive methods for the Voynich text: a ranked menu
Date: 2026-10-22. Scope: exploratory, data-driven methods that find structure in Beinecke MS 408 and turn it into testable hypotheses or candidate readings. Companion to REPORT_bioinformatics_signal.md, REPORT_emerging_methods.md, REPORT_linguistics_datasets.md and REPORT_imagery_symbology.md. Where one of those already specifies a method, this report gives only its inductive use and points back to it.
0. Purpose and ground rules
The deductive programme asks whether a named hypothesis reproduces the text. About 25 have been tested. Every cipher and generator family fails at least one held-out statistic, and none has produced a reading. Inductive methods ask the other question: what structure is in the text, and what does it suggest? Each one produces a candidate: a cluster, an alignment, an ordering, an anomaly list or a grammar. The candidate becomes a hypothesis in framework/hypotheses.yaml and is then tested on material the method never saw.
Exploration on a small, heavily studied text is where false discoveries come from. Every method below is therefore run under five rules:
- Planted-structure control. The method must first recover a structure planted in a reference text laid out on the manuscript's own pages, such as a topic, a paradigm, a reordering or an image-word link. This is the same logic as the programme's planted-key ladders. If the method cannot find a planted effect at the manuscript's size, its silence on the manuscript means nothing.
- Shared nulls (section 6b): glyph, word, line and page shuffles, the six generators plus the mixed-key and Naibbe-type simulators, and reference languages, all laid out with the same page geometry.
- Stability. A candidate counts only if it survives a bootstrap over sheets and a change of transliteration (ZL in EVA against GC in v101).
- Split by bifolium. Exploration and confirmation halves are split by bifolium, stratified by section and Currier language. Candidates are registered before the confirmation half is opened.
- Layout layer. Variant choice depends on line position (T21c). Every word-level method is therefore run twice: on raw forms, and on forms with line-conditioned variants merged. A candidate that appears only in raw forms is a layout effect, not a content effect.
Citation tags. VERIFIED-FETCHED means I read the page or abstract. VERIFIED-URL means the bibliographic record was confirmed (Crossref, ACL Anthology, arXiv or a publisher page) but the content was not read. UNVERIFIED means the citation comes from memory. "Not found" for prior Voynich use means my searches of arXiv, the ACL Anthology, the CEUR VOY2022 volume, voynich.ninja and the sibling reports turned up nothing. It does not mean nobody has ever tried.
Hypothesis families used in the ranking:
| Code | Family | |---|---| | LANG | natural language in some orthography | | CIPH | cipher of a natural language (homophonic, verbose, mixed key, nomenclator) | | GEN | meaningless generation (self-copying, grille, slot table) | | ORTH | spelling layer: Currier A/B, variant choice, line-conditioned spelling | | PROD | production: scribes, copying, order of writing, binding and page order | | CONT | content: what a page or section is about (candidate readings) | | LAYOUT | list, table or formula structure carried by the page geometry | | TRANS | transliteration reliability and glyph inventory |
1. Prior inductive work on the Voynich text
| Work | Method | Main finding | What it leaves open | |---|---|---|---| | Reddy & Knight 2011 | Linguistica morphology, 10-class word HMM, Sukhotin vowels, page similarity | Affix-like structure. Word bigrams add little. | No nulls beyond shuffles. Classes never tested against line position. | | Montemurro & Zanette 2013 | Information carried by a word's spread across sections; cosine co-occurrence network | Keywords (shedy, qokeedy, daiin, chedy); optimal scale about 800 words; herbal–pharmaceutical link | Words were placed in the authors' own section blocks, not page-level metadata. No scribe control. | | Amancio et al. 2013 | Network and intermittency statistics | Profile compatible with language (per sibling report) | Single-scale; no generators. | | Hauer & Kondrak 2016 | Language ID plus anagram decoding | Hebrew ranked first; methods disagree | Assumes one-to-one substitution, which the programme has rejected. | | Timm 2014; Timm & Schinner 2020 | Word-similarity networks; self-citation generator | Similar words cluster in place | Generator fails held-out statistics (T15; Rozanova & Temerev 2026). | | Davis 2020 | Palaeographic scribe study | Five hands | Text-side tests cover only three hands (Farrugia et al. 2022). | | Sterneck, Polish & Bowern 2021 | LDA, LSA and NMF on pages, 2–6 topics; correspondence analysis on metadata | LDA gave one dominant topic. NMF split A from B. Topics, hands and languages do not coincide one-to-one. | No held-out likelihood, no stability across seeds, no metadata-aware model. | | Farrugia, Layfield & van der Plas 2022 | Supervised scribe classifiers on glyph n-grams | SVM 90% with trigrams. All classifiers disagree with Davis on f65v, f85r, f86v, f95r, f95v. | Supervised, three hands only. | | Caruana, Layfield & Abela 2022 | Directional word-pair skew | Skew about 2× shuffled; languages higher | Single statistic. | | Zattera 2022 | Slot alphabet | Positional word grammar; "multiple languages" | Grammar fitted by hand. | | Painter & Bowern 2022 | NeighborNet on 110 glyph-form characters, 52 Latin manuscripts + 5 Voynich hands | Hands closest to Beneventan in shape; no single tradition | Phylogeny of letter forms, not of pages or text. | | Perone 2016 (blog) | word2vec + t-SNE | Visual clusters of similar-looking words | No evaluation. | | Lhotka, Salvi & Lazauskas (EPFL course paper) | fastText for ambiguous transliterations | fastText 86% on synthetic Italian/Latin ambiguities; word2vec poor at this size | Embedding semantics not tested. | | quimqu 2025, voynich.ninja thread 4834 | LDA (5), BERTopic (5), NMF (3) on pages | Biological and cosmological pages uniform; herbal mixed | Topic counts set by hand; no null. | | quimqu 2025, thread 4998 | 5-word-window co-occurrence graph, modularity, assortativity | Modularity about 0.25, between Latin treatises and narrative prose; Timm's generated text sits in the same place | Statistic does not separate the manuscript from a generator. | | Davis (with Layfield), DHQ; Layfield & Davis 2026, Digital Medievalist | LSA coherence of adjacent text blocks; similarity-maximising resequencing of Q13 and Q20 | Adjacent blocks beat shuffled ones. Coherence drops sharply at A/B changes. Proposes single-bifolium quires. | Timm (thread 5911): no permutation null and no calibration on shuffled known text for the resequencing step. | | Tauber 2026 | BPE merges as a structural probe | Slot purity 80.6%, near abugidas | One feature. | | Rozanova & Temerev 2026 | Joint diagnostics on units | Glyph h2 ≈ 2.7 bits; next-token prediction < 1% of token entropy; edge-glyph MI ≈ 0.2 bits; uncertain spaces physically narrower (AUC 0.905); 70% singleton types | Diagnostic, not generative. | | Anonymous 2026 (Zenodo 18122822) | Levenshtein clustering of the 30 labels on f70v2 | Morphological families with spatial bias around the wheel | One page; no null. |
Topic models and embeddings so far. Five topic studies are known: Sterneck et al., quimqu, the two Davis/Layfield LSA papers, and Montemurro & Zanette's keyword networks, which act as a topic model in all but name. All of them use whole pages as bag-of-words documents and choose the number of topics by hand (2–6). None reports held-out likelihood, stability across random seeds, or a model that conditions on scribe, Currier language or quire. Only NMF in Sterneck et al. and the DHQ LSA paper set the result against external metadata, and in both the A/B split dominates. For embeddings there are two small studies: Perone's word2vec with t-SNE, and the EPFL fastText paper, which framed embeddings as a transliteration-cleaning tool. Neither measured neighbour stability or aligned two embedding spaces. The programme's own T6 form-function test already uses context-neighbour sets, which are embeddings in all but name. I found no Voynich use of structural, author-topic, seeded/anchored, correlated, HDP or block-model topic models, and no embedding alignment between Currier languages or between scribes.
2. From pattern to reading
An inductive output becomes useful when it makes a prediction about material it has not seen. There are five kinds of output:
| Output | Example | How it becomes a hypothesis or reading | |---|---|---| | Partition | Word classes, page clusters, topic assignments | "Cluster k is the vocabulary of root-drawn herbal pages." Predict its occurrence on held-out pages from their drawings. | | Alignment | Word A ↔ word B; word ↔ visual feature; passage ↔ passage | "A-word x is the B spelling of y" or "w names a root form." Predict substitutions or features in held-out pages. | | Ordering | Seriation of pages or bifolia | "Bifolium order was X." Check against stains, offsets and quire signatures. | | Anomaly | Lines or pages that fit nothing | "f.. line n is a key, title or later addition." Check script, ink and position. | | Grammar | Paradigms, motifs, profile HMMs | "Endings -dy/-in/-ol form inflection classes." Predict which unseen stem–ending pairs occur. |
The manuscript has one source of semantic ground truth that most undeciphered scripts lack: its illustrations, with labels placed next to drawn objects. The ZL file has about 1,165 label tokens (843 types). Q20 has 324 marginal stars that track paragraphs on most pages. The zodiac pages have nymph labels around the figures, and the herbal section has 129 pages, each with one plant. Methods that use these anchors are weakly supervised. They are the only route to a reading that can be scored on held-out pages, which is why the text–image methods rank first.
3. Methods by field
Each entry gives what the method would reveal, its inputs, the null or control it needs, the hypothesis or reading it could generate, effort (one person's hours including controls, compute excluded), and prior Voynich use.
3.1 NLP: topics, embeddings, morphology
N1. Structural topic model with page metadata. Roberts, Stewart & Tingley 2019. Also covers Dirichlet-multinomial variants and the author-topic model of Rosen-Zvi et al. 2004.
- Reveals: Topic prevalence as a function of section, Currier language, hand, quire and sheet, with all of them in one regression. It also gives a "content covariate" estimate of how each hand changes word choice within a topic. That separates what is written from who wrote it and how it is spelled, the confound Sterneck et al. could only describe.
- Inputs: Page-by-word counts, also run at paragraph level; page metadata from the IVTFF headers (I, L, H, Q, sheet).
- Null/control: Metadata permuted within quire (keeps physical structure); topics fitted on word-in-page shuffles; the generators. Planted control: a Latin herbal-plus-recipe text laid out on the manuscript pages, enciphered with a planted A/B-style respelling assigned to "hands" — the model must recover topic and respelling as separate effects.
- Generates: (a) If topic prevalence is explained by section and the hand effect sits in the content covariate, A/B is spelling (ORTH), not subject. (b) A topic that crosses section boundaries, for example a herbal-B topic shared with Q13, is a CONT candidate ("these herbal pages are about bathing or preparation"). (c) Pages whose topic disagrees with their illustration are binding or misplacement candidates (PROD).
- Effort: 16 h.
- Voynich prior: Not found. Sterneck et al. used plain LDA, LSA and NMF with post hoc correspondence analysis.
N2. Hierarchical stochastic block model topics. Gerlach, Peixoto & Altmann 2018.
- Reveals: A topic model that treats the corpus as a bipartite page–word network and infers the number of topics and a hierarchy of word groups by model selection. Hand-picked K, the weak point of every Voynich topic study, goes away. The word hierarchy can be compared directly with the slot grammar: do word groups follow prefixes and suffixes (orthographic) or cut across them (topical)?
- Inputs: As N1.
graph-toolimplementation. - Null/control: Description length on the manuscript against degree-preserving rewired networks and against generators. Planted topics in a reference text.
- Generates: Inferred depth and width of the word hierarchy as a family statistic (LANG vs GEN). Groups that cut across slot classes are CONT candidates.
- Effort: 8 h.
- Voynich prior: Not found.
N3. Anchored and seeded topics from illustration anchors. Gallagher et al. 2017 (anchored CorEx); seeded LDA (Jagarlamudi, Daumé & Udupa 2012, UNVERIFIED).
- Reveals: Whether vocabulary anchored to one illustration type spreads coherently to unanchored pages. Examples: zodiac labels (Lz), pharmaceutical container labels (Lf), nymph labels (Ln).
- Inputs: Anchor word sets taken only from labels of one diagram type; paragraph text everywhere.
- Null/control: Random anchor sets of the same frequency profile. A reference control: anchor a Latin herbal topic with plant-name labels and check that the topic finds plant-description paragraphs.
- Generates: "Pages X, Y carry pharmaceutical-label vocabulary in their paragraphs" is a CONT reading: those paragraphs discuss the labelled containers or plant parts. It also yields a direct test of whether labels share vocabulary with running text more than chance, which bears on whether labels are names (LANG/CIPH) or decoration (GEN).
- Effort: 10 h.
- Voynich prior: Not found.
N4. Line-level short-text topics. Biterm topic model, Yan et al. 2013.
- Reveals: Topic shifts inside a page. Herbal and recipe paragraphs could be multi-part entries (name, description, use) or uniform. A biterm model handles documents of 8–12 words, which plain LDA cannot.
- Inputs: Lines and paragraphs with position-in-paragraph metadata.
- Null/control: Line order shuffled within page; generators. A Latin recipe collection laid out on Q20 geometry should show a "first-line topic" (title or ingredient) if the method works.
- Generates: "Paragraph line 1 carries a different topic from lines 2+" is a LAYOUT/CONT hypothesis (entry headings). It interacts with the known gallows-initial first lines: does the first line differ in vocabulary, not just in its first glyph?
- Effort: 8 h.
- Voynich prior: Not found.
N5. Stable small-corpus embeddings and cross-space alignment. PPMI-SVD (Levy, Goldberg & Dagan 2015) with bootstrap stability (Antoniak & Mimno 2018); fastText subword vectors (Bojanowski et al. 2017) as an orthography-only comparison; orthogonal Procrustes alignment (Hamilton, Leskovec & Jurafsky 2016).
- Reveals: (a) Neighbour sets that survive bootstrap, which at 34k tokens may be a few hundred words at most. (b) An alignment of the Currier A space onto the B space, and of each hand onto the others, giving a candidate translation table between "languages". If B is A respelled, the table maps words to words with a consistent glyph-level rewrite. If B differs in subject, aligned pairs are unrelated in form.
- Inputs: Word sequences with layout-normalised forms (rule 5); minimum count about 10; window 2–4 within lines.
- Null/control: Align A to a word-shuffled A of the same size (alignment floor). Positive control: Latin split in two, half respelled by a planted rule (for example -us→-os, qu→k), aligned at matched size. The method must recover the rule. Stability: Jaccard of top-5 neighbours across 50 bootstraps.
- Generates: A ranked list of A↔B word pairs and the edit operations that link them. A recurring operation (say an A suffix systematically aligned to a different B suffix) is an ORTH hypothesis, testable on held-out herbal A and B pages of the same plant type. If aligned pairs show no consistent edit, it supports different content or a different system.
- Effort: 14 h.
- Voynich prior: Embeddings partly (Perone; EPFL). Alignment between A and B not found.
N6. Paradigm discovery and Kober grids. Kober 1946; the paradigm discovery problem of Erdmann et al. 2020; MDL morphology (Creutz & Lagus 2007) and adaptor grammars (Johnson, Griffiths & Goldwater 2007) as segmenters.
- Reveals: Whether stems and endings form inflection classes: groups of stems that take different, partly overlapping sets of endings, with gaps that follow frequency. Alice Kober's triplets in Linear B were exactly this, three forms of one word sharing a stem with alternating endings and a "bridging" sign. A slot table predicts something else: a fully crossed stem × ending matrix with no class structure beyond chance gaps. The sibling reports propose Morfessor and adaptor grammars as segmenters. The inductive step here is biclustering the stem × ending incidence matrix and counting classes.
- Inputs: Segmentations from the programme's slot parse, from BPE and from Morfessor; the stem × ending count matrix.
- Null/control: The same matrix from slot-grammar and Naibbe-type simulators fitted to the manuscript (no classes by construction), and from Latin and Italian at matched type count (classes present). The null for gaps is independent fill with the observed stem and ending marginals.
- Generates: "Endings {-dy, -in, -ol} form class I; {-y, -ar, -al} class II" is a testable LANG/ORTH hypothesis: predict held-out stem–ending co-occurrence. A class split aligned with Currier language or hand would point to ORTH or PROD instead. Kober-style bridging glyphs at the stem–ending seam are candidate syllabic signs.
- Effort: 12 h.
- Voynich prior: Informal (Stolfi's and Zattera's word grammars; forum threads on word families). Formal paradigm induction with a class count against generators not found. Reddy & Knight ran Linguistica; Bowern & Lindemann note that full morphology induction was not attempted.
N7. Lower-priority NLP methods. Brown clustering (Brown et al. 1992), Clark's distributional–morphological classes (Clark 2003), dependency/constituency induction (Klein & Manning 2004) and compound PCFGs (Kim, Dyer & Rush 2019) all depend on word-order information. The programme has shown there is very little (T12 order gain; Rozanova & Temerev: under 1% of token entropy). They are worth one run each as a negative control for N5, about 6 h together. Cross-lingual decipherment models (Snyder, Barzilay & Knight 2010; Luo, Cao & Barzilay 2019; Luo et al. 2021) assume a one-to-one or near one-to-one character map, which the programme has rejected across 103 languages, so they rank low. Bayesian word segmentation (Goldwater, Griffiths & Johnson 2009) and unit discovery are already in the programme (useg.py, T22) and in the sibling reports.
3.2 Undeciphered scripts
U1. Context-vector glyph clustering, Copiale style. Knight, Megyesi & Schaefer 2011; sign clustering in Proto-Elamite, Born et al. 2019.
- Reveals: Which glyph units behave alike in left and right context, and are therefore candidates for allographs, homophones or one sign class. In the Copiale cipher, hierarchical clustering of left+right co-occurrence vectors (cosine distance) grouped the accented letters together and the unaccented Roman letters together. Once one member of a cluster was solved, the rest followed. That cluster map is what turned a stalled attack into a solution.
- Inputs: Glyph units under the core EVA grouping and under v101; separate left and right context vectors, also split by word position (initial, medial, final).
- Null/control: Glyphs shuffled within words; generator outputs; a Latin text under a planted homophonic key with known homophone sets (must be recovered).
- Generates: A candidate equivalence table, for example k~t, ch~sh, a~o in some positions. Each pair predicts that swapping the members leaves context statistics unchanged on held-out pages (CIPH homophones vs ORTH free variants vs LANG phonemes). The table is triangulated with U3 (parallel passages) and V1 (glyph images).
- Effort: 5 h.
- Voynich prior: Partly. Reddy & Knight's 2-state HMM and Sukhotin runs are coarse versions. Position-split context clustering with a planted-homophone control was not found.
U2. Positional and functional word classes, Indus style. Mukhopadhyay 2019; Yadav et al. 2010.
- Reveals: Word-level function from position and combination alone. Mukhopadhyay classified Indus signs by co-occurrence restrictions, fixed order, positional preference and occurrence in isolation, then glossed inscriptions by class, finding phrase-final and connective signs. Yadav et al. used n-grams to find frequent beginner and ender signs. For the Voynich text the units are words, and the positions are line-initial/final, paragraph-initial/final, label versus running text, and solo labels.
- Inputs: Word tokens with line, paragraph and label position; layout-normalised forms.
- Null/control: Word-in-line shuffles keep line composition but destroy position. Generators with the manuscript's line-length distribution. The same pipeline on Latin herbal and recipe text laid out on the pages: it must find Recipe, Item and et as positional or functional classes.
- Generates: Classes such as "label-only words" (candidate names), "paragraph-final words" (candidate formulae like et cetera or quantities) and "line-initial non-gallows words". Each class is a CONT or LAYOUT hypothesis with a held-out prediction. Label-only words are tested by N3 and V2.
- Effort: 8 h.
- Voynich prior: Partial. Line-position glyph effects are well studied (Feaster 2022; programme T21c). A word-level functional class inventory with nulls was not found.
U3. Parallel passages and substitution tables. Rongorongo parallel-text method (Butinov & Knorozov, UNVERIFIED; Pozdniakov & Pozdniakov 2007, UNVERIFIED); parallel-passage detection in the Hebrew Bible (Naaijer & Roorda 2016); text-reuse detection (Smith, Cordell & Mullen 2015).
- Reveals: Near-identical passages across pages, and above all which units substitute for which inside aligned parallels. In rongorongo, parallels showed which signs stand in for each other, giving allographs and ligature decompositions. The sibling report specifies Smith–Waterman alignment to test self-citation. The inductive product here is different: the substitution matrix observed inside high-scoring alignments.
- Inputs: Lines and paragraphs as glyph sequences; local alignment with gap penalties; alignment scores against the Gumbel null.
- Null/control: Shuffled lines; self-copy generator output, which produces parallels with random substitutions; Latin with scribal variation, which produces parallels with orthographic substitutions.
- Generates: A substitution table independent of U1. Agreement between U1 (context) and U3 (parallels) on the same pairs, for example ok~ot, is strong evidence of equivalence classes (ORTH/CIPH). Disagreement points to self-copying with arbitrary changes (GEN). Parallel clusters also mark repeated formulae (LAYOUT/CONT), such as recipe incipits.
- Effort: 14 h, shared with the sibling report's item 1.
- Voynich prior: Near-repeats studied by Timm (as self-citation). Substitution tables from parallels were not found.
U4. Kober–Ventris grid factorisation of glyph alternations. Kober 1946; Ventris's grid (UNVERIFIED as a citation; standard history).
- Reveals: Whether glyph alternations in minimal pairs factor into two independent dimensions, as consonant × vowel did for Linear B. Build a glyph × glyph matrix of alternation counts in fixed frames (the programme's minimal-pair frames from T21c), then fit a low-rank or bipartite block model. An alphabet gives one-dimensional structure. A syllabary written with multi-glyph units can give a two-way grid.
- Inputs: Minimal-pair alternation counts by frame position.
- Null/control: Alternation counts from slot simulators, which give structure by slot, not by grid. A Japanese kana text transliterated into romaji-like digraph units makes a positive control with a true grid.
- Generates: A grid assignment, for example rows = gallows type, columns = following vowel-like glyph. That is a direct LANG/CIPH hypothesis about phonetic value classes, testable by whether held-out alternations respect the grid.
- Effort: 10 h.
- Voynich prior: Not found.
U5. Short-document topic and sign co-occurrence for labels. Born et al. 2019; Monroe, Kelley, Born & Sarkar 2025.
- Reveals: In Proto-Elamite, LDA and hierarchical sign clustering on short tablets reproduced manual results and found new sign relations. The Voynich analogue treats each diagram (a zodiac page, a pharmaceutical page, a rosette) as a document of labels.
- Inputs: Label tokens grouped by page and label type (Lz, Lf, Ln, Ls, Lc).
- Null/control: Labels permuted between pages of the same type.
- Generates: "Zodiac labels share a sub-vocabulary that differs by month" is a CONT hypothesis, predicting label vocabulary on held-out zodiac pages from their sign. The anonymous f70v2 study did this for one page.
- Effort: 6 h.
- Voynich prior: One page (Zenodo 2026). Not found across label types.
Rao et al. 2009's conditional-entropy argument is already covered by the programme's entropy profile (T1, T12) and is not repeated.
3.3 Bioinformatics
B1. Profile HMMs for word families. Eddy 1998; multiple sequence alignment.
- Reveals: Treat a word family like a protein family, for example everything matching
q?ok[e]*d?y. Align its members, build a profile HMM with match, insert and delete states, and score every word in the manuscript. The fitted profile shows which positions are obligatory, which are optional and which insertions recur, a statistical version of Zattera's slots per family. Families that need different profiles are evidence of different generating rules. - Inputs: Word families seeded from edit-distance clusters or from N6 classes.
- Null/control: The same pipeline on slot-simulator output, where one profile should fit every family, and on Latin inflected families, where profiles differ by stem class.
- Generates: Family-specific templates (GEN vs LANG). Words that score high under two family profiles are candidate ambiguities. Family membership is a feature for N1 and V2.
- Effort: 8 h.
- Voynich prior: Not found.
B2. Page phylogenetics and stemmatics. Barbrook et al. 1998; NeighborNet (Bryant & Moulton 2004); δ-plots for tree-likeness (Holland et al. 2002); benchmark evaluation of stemmatic methods (Roos & Heikkilä 2009).
- Reveals: Whether pages are related by descent (each written by modifying an earlier one) or by shared topic. Characters are presence/absence of word types and variant choices per page. A copying chain produces strong tree-like signal (low δ) that follows writing order. Topical sharing produces reticulate, network-like signal.
- Inputs: Page × character matrix; layout-normalised forms.
- Null/control: The self-copy generator laid out page by page (tree-like by construction); a Latin herbal (network-like); page-label permutation.
- Generates: A rooted network is an order-of-composition hypothesis (PROD), testable against the codicology and against seriation (A3). Tree-likeness itself discriminates between GEN-by-copying and LANG.
- Effort: 12 h.
- Voynich prior: Painter & Bowern 2022 did glyph-form phylogenetics against Latin scripts. Page-level stemmatics was not found.
B3. Motif discovery anchored at line and paragraph starts. MEME (Bailey & Elkan 1994). Specified in the sibling report, section 2.1. The inductive addition is to run it on line-initial and paragraph-initial windows only, where the programme has found the strongest positional effects. Recovered motifs are candidate formulae (LAYOUT). About 6 h.
k-mer spectra, NCD clustering, Sequitur and Re-Pair grammars, DFA and change-point detection are specified in REPORT_bioinformatics_signal.md and REPORT_emerging_methods.md and are not repeated here.
3.4 Stylometry
S1. Unsupervised Delta with bootstrap consensus. Burrows 2002; stylo (Eder, Rybicki & Kestemont 2016).
- Reveals: Distance structure among pages from most-frequent words and glyph n-grams, with no labels. Farrugia et al. trained supervised classifiers on three hands. Unsupervised Delta over all five hands, the Currier languages and the disputed folios asks whether the text itself proposes Davis's partition, a different one, or none.
- Inputs: Page or 500-token-window profiles of the 100–300 most frequent words; glyph 3-grams.
- Null/control: Generators (self-copy may produce spurious "hands" by drift); a multi-author Latin text cut into windows.
- Generates: Disputed-page assignments for palaeographic re-examination (PROD), and whether "hand" or "language" is the stronger text-level partition (ORTH vs PROD).
- Effort: 4 h.
- Voynich prior: Supervised version only (Farrugia et al. 2022).
S2. Rolling stylometry along the physical book. Eder 2016.
- Reveals: Where the text's "voice" changes along the page sequence, at window resolution rather than page resolution. Mixed pages, A/B transitions inside a page or quire, and gradual drift all show up as a classification ribbon.
- Inputs: Sliding windows of 300–500 tokens in the current binding order and in alternative orders (A3, Layfield & Davis); reference sets of pure-A and pure-B pages.
- Null/control: Page-order permutations within quire; generator output with an A→B parameter drift.
- Generates: Sharp transitions at bifolium edges point to separate work units (PROD). Gradual drift within a quire points to a single scribe's changing practice, which supports an A→B evolution hypothesis of the kind Timm & Schinner propose. Transitions inside a page are anomalies worth palaeographic checking.
- Effort: 5 h.
- Voynich prior: Not found.
S3. General Imposters verification. Koppel & Winter 2014; Kestemont et al. 2016.
- Reveals: "Same system?" questions answered by verification rather than clustering. Are the astronomical labels in the same system as herbal A? Is Q13 B the same as Q20 B? Is f116v's marginal text in the Voynich system at all? The method compares a target against random feature subsets of a candidate and of impostor texts.
- Inputs: Target and candidate segments; impostors drawn from the other sections and from generator output.
- Null/control: Calibrate the score on Latin texts by known same and different authors at the same lengths.
- Generates: Explicit verification probabilities that resolve PROD and ORTH questions segment by segment.
- Effort: 8 h.
- Voynich prior: Not found.
S4. Stylochronometry. Stamou 2008. Ordering by gradual change in feature use. This is folded into A3 (seriation), which formalises it.
3.5 Archaeology: seriation and correspondence analysis
A3. Seriation of pages and bifolia with a proper null. Petrie 1899; Kendall 1971; spectral seriation (Atkins, Boman & Hendrickson 1998); the R package seriation (Hahsler, Hornik & Buchta 2008).
- Reveals: An ordering of pages or bifolia in which feature use (word types, variant preferences, ch/sh ratios, -edy rate) changes as smoothly as possible. In archaeology this recovered the relative dating of graves from pottery types. Here it gives an order-of-writing hypothesis that does not assume the current binding.
- Inputs: Page × feature abundance matrix; bifolium-level aggregates (conjugate leaves kept together); alternative feature sets (vocabulary, spelling only) to separate content order from spelling order.
- Null/control: The objective (anti-Robinson loss, or spectral gap) compared with random orders, and with orders recovered from generator text produced in a known order. Calibration on a known-order Latin text cut into pages and shuffled, which is the step Timm found missing in the LSA resequencing.
- Generates: (a) If the spelling-only seriation recovers the A→B gradient with a coherent order, that is an ORTH/PROD hypothesis: a spelling practice that evolved. (b) If seriated neighbours are conjugate leaves more often than chance, it supports Layfield & Davis's single-bifolium quires. (c) Predicted adjacencies are checked against physical evidence: offsets, stains, quire marks and the programme's H-ORDER-BINDING result.
- Effort: 10 h.
- Voynich prior: Partly. Layfield & Davis 2026 resequenced Q13 and Q20 by LSA similarity, without a permutation null. Spectral seriation with calibration was not found.
A4. Correspondence analysis with supplementary metadata. Greenacre 2007; Baxter 2015.
- Reveals: One map with pages and words together. Words at the extremes of each axis say what distinguishes the axis. With section, hand and language entered as supplementary variables (projected, not fitted), the axes not explained by any metadata are where unlabelled structure lives.
- Inputs: Page × word table (frequent words), page metadata.
- Null/control: Inertia of each axis against word-in-page shuffles; generators.
- Generates: A residual axis that sorts herbal pages but follows neither hand nor language is a CONT candidate (for example plant type), handed to V2 for an image test.
- Effort: 4 h.
- Voynich prior: Sterneck et al. used multiple correspondence analysis on metadata and topic labels, not CA on the word table. Not found in this form.
3.6 Signal processing and physics
P1. Keyword detection by level statistics. Ortuño et al. 2002; Carpena et al. 2009.
- Reveals: Keywords from the clustering of a word's occurrences along the text, with no section labels or partition length. The statistic compares the spacing of occurrences with a geometric (random) distribution. Montemurro & Zanette needed a partition scale; this needs none, so it works at the page and paragraph scale where herbal entries live.
- Inputs: Token positions in physical order; frequency ≥ 5.
- Null/control: Shuffled text gives the reference spacing distribution analytically. Generators: self-copying produces local clustering for all words, so the test is whether clustering is word-specific beyond frequency.
- Generates: Per-page keyword lists. A herbal page's top keyword that occurs nowhere else is a candidate plant name (CONT), testable against N3 and V2 and against label vocabulary.
- Effort: 4 h.
- Voynich prior: Montemurro & Zanette 2013 is the entropy-based relative. Level statistics on the Voynich text was not found.
P2. Recurrence plots and recurrence quantification. Marwan et al. 2007; Webber & Zbilut 1994.
- Reveals: A recurrence plot of the word sequence (a dot wherever word i equals word j, or a line-similarity version) shows repeated passages as diagonals, topical sections as blocks and alternation as checkerboards. Determinism (share of recurrences on diagonals), mean diagonal length and laminarity quantify copying against topical persistence.
- Inputs: Word sequence; line-vector similarity matrix.
- Null/control: Self-copy generator (short diagonals near the main diagonal); Latin (blocks with few diagonals); word shuffles within page.
- Generates: The diagonal-length distribution and its distance from the main diagonal is a direct GEN-by-copying test. Off-diagonal diagonals far from the main diagonal are cross-page parallels, input for U3.
- Effort: 6 h.
- Voynich prior: Not found.
P3. Multifractal DFA on paragraph and word-length series. Kantelhardt et al. 2002; Drożdż et al. 2016.
- Reveals: Whether the series of paragraph lengths, or of word lengths in tokens, has the multifractal signature that narrative texts show in sentence-length series. Plain DFA is specified in the sibling report.
- Inputs: Paragraph-length and word-length series in physical order.
- Null/control: Shuffled and phase-randomised surrogates; the Zipf-preserving long-range surrogate (Montemurro & Degli Esposti 2026).
- Generates: A family statistic (LANG vs GEN). Low priority, because line and page geometry constrain these series.
- Effort: 5 h.
- Voynich prior: Not found (Landini's 2001 spectral work is the nearest).
P4. Burstiness and adaptation as a label-free topic-word detector. Church 2000; Altmann, Pierrehumbert & Motter 2009; Goh & Barabási 2008. The sibling report covers burstiness as a family test. The inductive use is to rank words by adaptation (how much a first occurrence raises the chance of a second in the same page) relative to frequency. High-adaptation, mid-frequency words are topic-word candidates that feed P1 and N3. About 3 h.
3.7 Network science
G1. Stochastic block models of word co-occurrence and succession. Karrer & Newman 2011; Peixoto 2014; Louvain (Blondel et al. 2008) as a baseline.
- Reveals: Community detection (Louvain) finds groups of words that co-occur. An SBM also finds roles: groups that connect to other groups in a fixed way, for example "words that are followed by group Y" in a directed succession graph. Roles, not communities, are what syntax looks like in a network.
- Inputs: Directed word-succession graph within lines; undirected same-line co-occurrence graph; layout-normalised forms.
- Null/control: Degree-corrected configuration model; generators. quimqu's 2025 graph found the Timm generator indistinguishable on modularity, so modularity alone is not a valid test.
- Generates: Disassortative blocks (A→B role patterns) beyond the null are LANG evidence and give candidate word classes. Their absence, with only assortative communities, supports topic-without-syntax (list or GEN).
- Effort: 8 h.
- Voynich prior: Graph modularity (quimqu 2025); networks (Amancio 2013; Timm). SBM roles not found.
node2vec (Grover & Leskovec 2016) and other graph embeddings add little over N5 at this size and are not ranked.
3.8 Information theory
I1. MDL comparison of metadata partitions. Two-part code length with a Krichevsky–Trofimov or Pitman–Yor word model.
- Reveals: Which partition of the pages best compresses the text: none, A/B, five hands, seven sections, quires, sheets, or the crossings. This is the cleanest single answer to "what does the vocabulary follow?" Model cost is charged for each extra partition cell.
- Inputs: Page word counts and metadata.
- Null/control: The same comparison on generators and reference texts with planted partitions.
- Generates: If sheets beat sections (z ≈ 16 sheet locality is already known), the unit of content is the sheet (PROD/CONT). If hand beats language once section is included, A/B is a property of scribes (PROD).
- Effort: 4 h.
- Voynich prior: Not found in this form.
NCD clustering (Cilibrasi & Vitányi 2005), Sequitur (Nevill-Manning & Witten 1997), Re-Pair (Larsson & Moffat 2000) and entropy-rate estimators are in the sibling reports. BPE (Tauber 2026) and unit discovery are already in the programme.
3.9 Ecology and statistics
E1. Unseen vocabulary, rarefaction and turnover. Good 1953; Efron & Thisted 1976; Chao 1984; Baselga 2010.
- Reveals: (a) The estimated total vocabulary of each section and hand. 71% hapax means a large unseen vocabulary, and the estimators turn that into numbers with intervals. The key contrast: a slot table has a bounded vocabulary (the product of the slot inventories), so richness estimators should converge, while language vocabularies keep growing. (b) Rarefaction curves at matched token counts across hands and sections. (c) Turnover against nestedness between pages (Baselga). A herbal with a shared formula vocabulary plus a page-specific plant name is nested plus a small turnover component. Independent page vocabularies are pure turnover.
- Inputs: Word-type frequency counts by page, section and hand.
- Null/control: Generators fitted to the manuscript (bounded or unbounded by construction); reference languages at 34k tokens.
- Generates: "Slot-bounded vocabulary" against "open vocabulary" is a GEN/CIPH/LANG discriminator with a cross-linguistic reference. The nestedness profile is a CONT/LAYOUT hypothesis (entry formula plus name).
- Effort: 4 h.
- Voynich prior: Not found (vocabulary growth and type/token ratios only).
E2. Single-page provenance test. Thisted & Efron 1987.
- Reveals: Thisted and Efron asked whether a newly found poem was Shakespeare's by predicting how many words it should contain that Shakespeare used 0, 1, 2… times before. Applied page by page, this asks whether each page's rare-word profile fits the rest of its section, hand or language. Misfits are candidates for a different source, scribe or system.
- Inputs: Leave-one-page-out frequency spectra.
- Null/control: The same test on reference-text pages and generator pages.
- Generates: A per-page outlier list (PROD), cross-checked against S1 and J1.
- Effort: 3 h.
- Voynich prior: Not found.
E3. Lost-leaf calibration with unseen-species models. Kestemont et al. 2022.
- Reveals: Kestemont and colleagues used Chao-type estimators to estimate lost medieval narratives from surviving witnesses. Here the "species" are page-level word types or word families, and the question is how much text is missing from each section. The manuscript has a ground truth: quire numbering shows missing leaves in known places. The estimator can be checked against it before being used on unknowns such as the size of the original herbal.
- Inputs: Type incidence across pages per section.
- Null/control: Calibrate by deleting known numbers of pages from reference texts and from the manuscript itself.
- Generates: Missing-content estimates per section (PROD), and a test of whether the known missing leaves were text-heavy.
- Effort: 6 h.
- Voynich prior: Not found.
E4. Capture–recapture across transliterations. Chao 1987.
- Reveals: Treat each independent transliteration (ZL, IT, CD, GC) as a capture of the true glyph sites. Agreement and disagreement patterns estimate how many uncertain readings no transliterator flagged. This sets an error floor for every inductive method that keys on rare words.
- Inputs: Aligned transliterations at line level.
- Null/control: Simulated transcriptions of a known text with planted error rates.
- Generates: A TRANS error model; words whose hapax status depends on a probable misreading are removed from N3, P1 and E1.
- Effort: 6 h.
- Voynich prior: Not found (transliteration comparison yes; capture–recapture estimation no).
3.10 Unsupervised machine learning
J1. Anomaly detection on lines and pages. Isolation forest (Liu, Ting & Zhou 2008), with UMAP (McInnes et al. 2018) for display only.
- Reveals: Lines and pages that fit no pattern: unusual glyph mixtures, word lengths, positional profiles or repetition. Candidates include keys, titles, colophons, later additions, and pages written in another system.
- Inputs: Per-line and per-page feature vectors (glyph n-gram rates, word-length moments, slot-violation counts, label/paragraph type, repetition).
- Null/control: Anomaly-score distribution on generator text and reference text laid out the same way; known anomalies (f116v, f1r's top line, the Q20 star-free paragraphs) as positive checks.
- Generates: A short ranked list for palaeographic and imaging review (PROD/TRANS). An anomaly that is also an S3 "different system" is a candidate key or plaintext fragment.
- Effort: 4 h.
- Voynich prior: Not found.
Page and line clustering with UMAP and HDBSCAN has been done (Sterneck et al.; BERTopic in quimqu). It adds little over N1 and A4.
3.11 Computer vision on the page images
V1. Glyph-image clustering as an independent allograph table. Self-supervised features (SimCLR, Chen et al. 2020; DINO, Caron et al. 2021); unsupervised CNN sign grouping (Corazza et al. 2022).
- Reveals: The sibling report specifies the image-to-EVA audit. The inductive use is twofold. First, a third, image-based allograph table to triangulate with U1 and U3. Second, the Corazza test applied to Voynich groupings: do Currier A and B, or the five hands, differ in glyph shape as well as in usage?
- Inputs: Segmented glyph crops from the Yale images, aligned to ZL lines.
- Null/control: Shape clusters against EVA labels permuted within line; a Latin manuscript with a known transcription.
- Generates: Glyph pairs that are distinct in usage but merge in shape, or the reverse. These are TRANS/ORTH hypotheses (for example, two EVA glyphs that are one sign written two ways).
- Effort: 40–60 h (segmentation dominates).
- Voynich prior: Davis 2020 (palaeography); sibling report. Self-supervised shape clustering tied to usage not found.
V2. Text–image correspondence on the herbal pages. Mantel test (Mantel 1967) and the RV coefficient (Robert & Escoufier 1976) for matrix agreement; word–region translation models (Duygulu et al. 2002; Barnard et al. 2003); CCA (Hotelling 1936); CLIP-style image embeddings (Radford et al. 2021) as an alternative to hand coding.
- Reveals: (a) Whether pages that look alike (plant drawings) also read alike, beyond what section, hand and language explain. That is a partial Mantel test between an image-similarity matrix and a text-similarity matrix, controlling for metadata matrices. (b) Which words go with which visual features: a translation model learns P(word | feature) for features such as root form (bulbous, branching, tuberous), leaf shape and arrangement, flower present, or paint colours. Barnard et al. and Duygulu et al. learned word–region lexicons from captioned images with exactly this machinery.
- Inputs: About 129 herbal pages, plus pharmaceutical pages with plant fragments. A feature table coded blind to the text by two coders (10–15 h of coding; inter-coder κ reported), or CLIP image embeddings. Text features from N1, N5 and P1.
- Null/control: Page labels permuted within section × hand × language cells, so a correspondence cannot ride on A/B or scribe. Positive control: an illustrated Latin herbal with transcription (the Pseudo-Apuleius tradition, see the datasets report), where the method must find plant-part words.
- Generates: Candidate readings in the strict sense: "word w is linked to bulbous roots, held-out AUC x". Each is tested by prediction: (i) predict visual features of held-out herbal pages from their text; (ii) predict that w appears in pharmaceutical labels next to drawn roots of the same form, a cross-section test the model never trained on. A null result with a working positive control is also informative. It says text and drawings were not composed together, which bears on GEN and on the "illustrations as decoration" view.
- Effort: 35 h including coding.
- Voynich prior: Not found. Plant identifications are qualitative. Turenne 2026 uses an LLM to align images with Pseudo-Apuleius herbals, not text features with image features.
V3. Star, figure and label attributes against text. Quire 20 and zodiac pages.
- Reveals: On Q20 the marginal stars match paragraph counts on most pages: f103v 14/14, f104r 13/13, f106r 15/15, with documented exceptions such as f108v (16 stars, about 8 paragraphs), f111r (17/6) and f111v (19/about 8) (voynich.nu Q20 notes). Stars differ in centre colour (red or yellow, often alternating) and in having a tail. Zodiac nymphs differ in dress, tub, held star and ring position. The test asks whether these attributes predict anything in the adjacent text: incipit word, paragraph length, vocabulary.
- Inputs: Star and figure attribute coding (about 6 h); paragraph and label text.
- Null/control: Attributes permuted within page; colour alternation modelled as a pure rhythm (period 2) as the default.
- Generates: If colour or tail predicts vocabulary, stars are category markers (CONT). If only the rhythm is present, they are decoration and paragraph markers. The exception pages, where stars outnumber paragraphs, are LAYOUT hypotheses: do long paragraphs there contain internal entry boundaries the stars mark? This is directly testable by looking for paragraph-initial vocabulary at star-aligned line starts.
- Effort: 8 h.
- Voynich prior: Counts are documented (Zandbergen's Q20 page). Statistical attribute–text tests not found.
Layout analysis, ink and stroke studies and multispectral imaging are covered in REPORT_imagery_symbology.md.
3.12 Music information retrieval
M1. Geometric repeated-pattern discovery. SIA/SIATEC (Meredith, Lemström & Wiggins 2002); COSIATEC (Meredith 2014).
- Reveals: Music pattern discovery treats a score as a set of points (time, pitch) and finds every pattern that repeats under translation. A Voynich page is also a point set: (position in line, line number) with a glyph or word-class value. SIATEC finds shapes that repeat anywhere on the page, such as vertical runs of the same glyph at line starts, diagonals and column-aligned word classes. COSIATEC's compression ratio measures how much of a page translated patterns explain.
- Inputs: Per-page point sets at glyph and word-class level, with x as glyph offset or token index.
- Null/control: Same-geometry pages from generators and from Latin manuscripts transcribed with line breaks; line order shuffled within page.
- Generates: Column-aligned patterns are LAYOUT hypotheses: pages that are tables written as prose, with fields in fixed columns. Feaster's rightward and downward gradients become specific shapes that can be tested on held-out pages. High compression on some page types and not others separates list pages from prose pages.
- Effort: 12 h.
- Voynich prior: Not found. Feaster 2022 and Stafford 2022 describe positional distributions, not translational patterns.
3.13 Cryptanalysis-adjacent tools
- Cipher-type classifiers (Nuhn & Knight 2014; Leierzopf et al. 2021). These classify among classical cipher types. None of their training classes covers verbose, mixed-key or generator text, so applied as published they would only report the manuscript as out of distribution. The useful version is a classifier trained on the programme's own simulators. That is the programme's T15 nearest-generator test and the sibling report's simulation-based inference item. Not ranked separately.
- Isomorphs. Already run (T11). Extension: isomorphs across hands and between labels and running text, about 3 h.
- Segmentation (Aldarrab & May 2022). Already absorbed into T22 and
useg.py. - Z340-style repeat profiles. Oranchak, Blake & Van Eycke 2024 describe the route to the Z340 solution. Row non-repeat anomalies and "pivots" came first, then a spike in bigram repeats at period 19 against a shuffle mean. Then came enumeration of "billions" of transposition schemes scored by repeat counts, with about 655,000 variants run through a solver. The programme has run 1-D periodicity (T11). The extension is the 2-D version: repeat profiles along columns and diagonals of each page, and along non-linear reading orders for the circular and rosette texts. About 6 h.
3.14 Practitioner and unconventional methods
The external breakthroughs share three habits that formal work often skips.
- Cluster first, then let a human recognise something. The Copiale solution came from the context-vector cluster map, then a person recognising CEREMONIE and DER, which showed the Roman letters were spaces. The machine narrowed the search; the human supplied the recognition. The Voynich equivalent is a concordance workbench: keyword-in-context views of any candidate (a U1 cluster, a P1 keyword, a V2 word) shown next to the page images, so specialists in herbals, astrology and recipes can say what the context suggests. It costs about 10 h to build on the shared data layer. Its output is unscored hypotheses that must enter the registry like any other.
- Exhaustive enumeration with a cheap score. The Z340 team succeeded by enumerating very large spaces of reading orders scored by a statistic that could be computed in microseconds. The equivalent here is enumerating reading orders, line orders and page orders scored by held-out predictability. This is cheap given T13's Kneser–Ney machinery.
- Archival and comparative search (OSINT). The 2023 decryption of Mary Stuart's letters (Lasry, Biermann & Tomokiyo) began with finding misfiled ciphertexts in an archive catalogue. For the Voynich manuscript, the analogue is large-scale visual retrieval of comparanda: other manuscripts with the same plant drawings, tubs or star layouts. The sibling report ranks CLIP/IIIF retrieval as historically valuable but blocked by access.
Forum practitioners (Stolfi's word grammar, Zattera's slots, Feaster's positional maps, the quimqu analyses) have produced most of the structural observations the programme now tests. They mostly lack nulls, not ideas. The battery in 6b supplies the nulls.
4. How the families are informed
| Family | Methods most able to move it | |---|---| | LANG | N6 paradigms, G1 roles, E1 bounded vocabulary, U4 grid, V2 correspondence | | CIPH | U1 + U3 + V1 triangulated equivalence tables, N5 alignment, U4 | | GEN | P2 recurrence diagonals, B2 tree-likeness, E1, N6 (fully crossed grids), U3 random substitutions | | ORTH | N1 content covariate, N5 A↔B alignment, A3 spelling-only seriation, S2 | | PROD | A3, S1–S3, B2, E2, E3, I1, J1 | | CONT | V2, N3, P1, N1, A4 residual axes, U2 label-only words, V3 | | LAYOUT | M1, N4, U2, B3, V3 exception pages | | TRANS | E4, V1, U1 |
5. Methods not recommended
- MUSE-style unsupervised alignment of Voynich embeddings to a known language. It needs large, comparable corpora. The sibling report notes no positive control at 34k tokens.
- LLM "readings". No consistency-tested result exists, and the outputs cannot be put under the shared nulls.
- Plain LDA with hand-picked K on pages. Already done three times; the problem was the model, not the data.
- t-SNE displays as evidence. Hyperparameter-sensitive, as Sterneck et al. note. Display only.
6. Recommendations
6a. Ranked top 15
Expected value (EV) is judged by three things: whether the output can be tested on held-out material, whether it discriminates between families, and whether anyone has done it. Cost is in hours. Methods sharing infrastructure are grouped.
| Rank | Method | EV | Cost (h) | Families informed or spawned | Why this rank | |---|---|---|---|---|---| | 1 | V2 Text–image correspondence (Mantel + word–feature translation model) on herbal pages | High | 35 | CONT, LANG, GEN | The only method that can yield a reading with held-out ground truth. A null with a working positive control is also publishable. | | 2 | N1/N2 Metadata-aware topic models (STM; hSBM) | High | 16 + 8 | ORTH, PROD, CONT | Separates subject, scribe and spelling, the confound that blocks interpretation of A/B. Replaces hand-picked K. | | 3 | N5 Stable embeddings with A↔B and hand↔hand alignment | High | 14 | ORTH, CIPH | Produces an explicit A→B rewrite table or rules one out. Planted-respelling control makes it decisive. | | 4 | N6 Paradigm discovery and Kober grids against slot simulators | High | 12 | LANG, GEN, ORTH | Inflection classes cannot come from a fully crossed slot table. Clean discriminator with a held-out prediction. | | 5 | E1–E4 Ecology bundle: unseen vocabulary, rarefaction, turnover, Thisted–Efron page test, lost-leaf calibration, transliteration capture–recapture | High | 19 | GEN, LANG, PROD, TRANS | Cheap, novel, calibratable on known missing leaves. Bounded vs open vocabulary separates slot generators from language. | | 6 | U1 + U3 Triangulated equivalence tables (context clustering + parallel-passage substitutions) | High | 19 | CIPH, ORTH, GEN | Two independent sources agreeing on glyph or word equivalences is the Copiale and rongorongo route. Disagreement favours GEN. | | 7 | A3 + A4 Seriation and correspondence analysis with calibration | Medium-high | 14 | PROD, ORTH | Tests the singulion proposal and A→B drift with the null it lacked. Predictions check against the physical book. | | 8 | U2 Positional and functional word classes | Medium-high | 8 | CONT, LAYOUT | Finds label-only names, formula words and list markers; feeds N3 and V2. | | 9 | S1 + S2 Unsupervised Delta and rolling stylometry | Medium | 9 | PROD, ORTH | Cheap. Locates transitions at sub-page resolution; resolves disputed folios. | | 10 | P1 + P4 Label-free keywords (level statistics, adaptation) | Medium | 7 | CONT | Per-page keyword lists are the raw material for plant-name candidates. | | 11 | V3 Q20 star and zodiac figure attributes against text | Medium | 8 | CONT, LAYOUT | Small, concrete, uses documented counts. Exception pages give testable entry-boundary hypotheses. | | 12 | P2 Recurrence quantification | Medium | 6 | GEN, PROD | Direct, visual copying test; feeds U3 with cross-page parallels. | | 13 | J1 Anomaly detection | Medium | 4 | PROD, TRANS | Cheap; finds keys, additions and foreign pages for review. | | 14 | M1 SIA/COSIATEC 2-D pattern discovery | Medium | 12 | LAYOUT, GEN | Novel transfer; tests whether some pages are tables. | | 15 | B2 Page phylogenetics with tree-likeness | Medium | 12 | GEN, PROD | Tree signal discriminates copying chains from topical sharing; gives a composition-order hypothesis. |
Next in line: G1 SBM roles (8 h), U4 Kober–Ventris grid (10 h), I1 MDL partitions (4 h), S3 General Imposters (8 h), B1 profile HMMs (8 h), U5 label documents (6 h), N3 anchored topics (10 h; promote if V2 coding is done, since it uses the same anchors), N4 biterm (8 h).
Total for the top 15 is about 235 h. The cheap first pass (ranks 5, 9, 10, 12, 13 and I1) is about 50 h and needs no image work.
6b. Inductive battery design
Shared data layer. One relational store built once from the IVTFF files through the existing corpus.py/ivtff.py loaders. All methods read it; none re-parses the text.
| Table | Key fields |
|---|---|
| page | folio, side, quire, sheet/bifolium id, conjugate folio, position in quire, section (I), Currier language (L), hand (H), illustration codes (from V2/V3 coding), image file and IIIF region |
| para | page, paragraph index, first/last flags, star id and attributes (Q20), line count |
| line | page, para, line index in page and paragraph, locus type (P0, Pb, Lz, Lf, Ln…), first/last flags, token count, image bounding box when available |
| word | line, index in line, form in ZL, GC and IT (aligned), layout-normalised form, uncertain-space-before flag, slot parse, family id (B1), is-label |
| glyph | word, index, unit under core grouping and v101, position class (initial/medial/final) |
| feature | per-page visual features (coded and embedded), per-star and per-figure attributes |
Shared corpora laid out on the same pages. Every comparison corpus is written into the manuscript's own page, paragraph, line and label geometry using generators.layout_of/fill, with the same metadata columns filled by the layout it occupies.
| Code | Corpus | |---|---| | R0 | Voynich, ZL; R0g the same in GC | | N-glyph | glyphs shuffled within word | | N-wline | words shuffled within line | | N-wpage | words shuffled within page | | N-lpage | lines shuffled within page | | N-page | page order permuted within quire, conjugate leaves kept together; and within section | | N-meta | metadata labels circularly shifted along the physical order (keeps autocorrelation, breaks alignment) | | N-zipf | Zipf-preserving long-range surrogate (Montemurro & Degli Esposti 2026) | | G1–G6 | the six generators, fitted per Currier language | | G7–G8 | mixed-key (Tranchedino) and Naibbe-type simulators of Latin/Italian genre text | | L-ref | 103 reference languages at matched length; plus genre-matched Latin herbal, recipe and astrological text | | P-plant | planted-structure versions of L-ref: topic, respelling, paradigm, reordering, image–word link, homophone sets |
Method contract. Each method is a module that takes a corpus id and returns three things:
- Statistics, each with its null distribution from the matching N-corpus and its position against G and L.
- Candidates (clusters, alignments, orderings, anomalies, grammars) in a common JSON schema. Each candidate carries a stability score: bootstrap over bifolia (B = 200), ZL vs GC agreement, and raw vs layout-normalised agreement.
- A hypothesis card for
hypotheses.yamlwith a prediction stated on the confirmation half.
Gates before a candidate is registered. (i) The planted version is recovered at the manuscript's size. (ii) The statistic lies outside the 95% band of the relevant N-corpus. (iii) Stability ≥ 0.7 (Jaccard or adjusted Rand, depending on output type) across bootstraps and transliterations. (iv) The candidate is not reproduced by any G corpus at the same rate. (v) Candidate lists are FDR-controlled at q = 0.1.
Exploration and confirmation split. Bifolia are split in two within each quire, alternating, stratified by section and language, and fixed with a hash before any method runs. Inductive methods see only half E. Candidates are frozen and registered. The deductive harness then scores them on half C. Results on half C enter the book; results on half E are reported as exploratory.
Run order.
- Data layer, alignment of transliterations, layout-normalised forms, corpus generation (12 h).
- Cheap descriptive pass: E1–E4, P1, P4, J1, I1, S1, S2, P2 (about 50 h).
- Representation pass: N1/N2, N5, U1, U3, A3/A4 (about 80 h).
- Grammar pass: N6, B1, U4, G1 (about 40 h).
- Image pass: V2/V3 coding, then V2, V3, N3 (about 55 h).
- Triangulation: candidates found by two or more independent methods (for example U1 + U3 + V1 on an equivalence, or N3 + P1 + V2 on a plant-name candidate) are promoted first.
Concordance workbench. A read-only view over the data layer (KWIC lines plus image crops) for each registered candidate, so specialist readers can comment before the confirmation test. Comments are logged as hypotheses, never as results.
6c. Gaps: methods not found applied to the Voynich text
From the searches described in section 0, none of the following has a Voynich application:
- Metadata-aware topic models (structural, author-topic, Dirichlet-multinomial regression); hierarchical SBM topic models; anchored or seeded topics; short-text (biterm) topics at line level.
- Stability-tested embeddings, and alignment of embedding spaces between Currier languages or between hands.
- Formal paradigm discovery with inflection-class counts against slot simulators; Kober–Ventris grid factorisation of glyph alternations.
- Copiale-style context clustering with planted-homophone controls; substitution tables from aligned parallel passages; triangulation of equivalence tables across context, parallels and glyph images.
- Word-level positional and functional class inventories in the Indus manner.
- Profile HMMs for word families; page-level stemmatics and tree-likeness (δ) tests.
- Unsupervised Delta over all hands; rolling stylometry; General Imposters verification of sections, labels and marginalia.
- Calibrated seriation of pages or bifolia (the LSA resequencing exists without a null); correspondence analysis of the page × word table with supplementary metadata.
- Level-statistics keyword detection; recurrence plots and recurrence quantification; multifractal DFA.
- Stochastic block models for word roles.
- MDL comparison of metadata partitions.
- Unseen-vocabulary estimation, rarefaction and turnover/nestedness; the Thisted–Efron single-page test; unseen-species estimates of lost content calibrated on the known missing leaves; capture–recapture across transliterations.
- Isolation-forest anomaly ranking of lines and pages.
- Quantitative text–image correspondence (Mantel, RV, CCA, word–feature translation models) on herbal pages; star-attribute and figure-attribute tests against text in Q20 and the zodiac.
- Geometric pattern discovery (SIA/SIATEC/COSIATEC) on page layouts.
- 2-D (column, diagonal, circular) repeat profiles in the Z340 manner.
Done but thin: page-level LDA, LSA, NMF and BERTopic (four studies, no held-out evaluation); word2vec and fastText (two small studies); co-occurrence graph modularity (one forum study, generator not separated); supervised scribe classification (three hands); label clustering (one page).
7. Sources
Voynich-specific
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Topic models, embeddings, morphology, grammar
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Decipherment and undeciphered scripts
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- Monroe, Kelley, Born & Sarkar 2025. Recent progress in deciphering Proto-Elamite. Near Eastern Archaeology 88(4): 314–323. DOI 10.1086/738240 — VERIFIED-URL
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- Lastilla, L., Ravanelli, R., Valério, M. & Ferrara, S. 2021. Modelling the Rongorongo tablets. DSH 37(2): 497–516. DOI 10.1093/llc/fqab045 — VERIFIED-URL
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Cryptanalysis and practitioner cases
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- Oranchak, D., Blake, S. & Van Eycke, J. 2024. The solution of the Zodiac Killer's 340-character cipher. arXiv:2403.17350 — VERIFIED-FETCHED
- Lasry, G., Biermann, N. & Tomokiyo, S. 2023. Deciphering Mary Stuart's lost letters from 1578–1584. Cryptologia. Coverage: https://phys.org/news/2023-02-codebreakers-decipher-lost-letters-mary.html — VERIFIED-URL (news record; DOI not confirmed)
- Ravi, S. & Knight, K. 2011. Bayesian inference for Zodiac and other homophonic ciphers. ACL. https://aclanthology.org/P11-1025/ — VERIFIED-URL
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Bioinformatics, stemmatics, stylometry
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Seriation, ecology, statistics
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Signal processing, networks, information theory, ML, vision, music
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