Computational Analysis of the Voynich Manuscript

Natural language, cipher, or artificial system? An investigation using information theory, machine learning, and computational statistics.

Independent research project | Corpus: STA1 2.0 (37,087 words, 157,254 glyphs, 166 distinct glyphs)

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A 5-minute introduction (no maths required) · Introducción en 5 minutos (sin matemáticas)

English

The Voynich Manuscript is a 240-page illustrated book written around 1404–1438 in an alphabet nobody else has ever used. For 600 years scholars, codebreakers and amateurs have tried to read it, and all of them have failed. This project is a systematic computational attempt — and an honest report of where the text breaks down.

What we did. We treated every standard hypothesis as a testable prediction and we ran them all: that it is a natural language in disguise (Hebrew, Aramaic, Arabic, Tibbonid Hebrew, Judeo-Arabic, Ge'ez), that it is a classical cipher (substitution, polyalphabetic, transposition, nomenclature codes), that it is nonsense, that it is a constructed language. Nineteen substitution models, five Semitic targets, three writing-system types — all of them hit the same wall.

What we found.

• The text is real. It has a rigid internal structure that no random gibberish reproduces; in particular, glyphs are position-locked inside the word at a level twice as strong as any natural language we measured.
• It is not a hidden natural language. Every model that tries to map glyphs to letters of a real alphabet stalls at the same ceiling: a few valid roots and at most ~68 % valid bigrams.
• It is a positional code. What matters is the position of a glyph in the word, not the glyph's "letter value". This pattern matches a 17th-century theoretical category — Caramuel's cifra ineffabilis / philosophical pasigraphy — that traces back to Ramon Llull and to medieval Aristotelian/Kabbalistic combinatorics.
• One folio is special. Folio f57v ("the Venus ring") contains five glyphs that appear nowhere else in the manuscript — a private subalphabet whose iconography matches the karacteres described in the medieval astrological treatise Picatrix.
• The grammar can be reconstructed. Each Voynich word follows a fixed 5-slot template: DOMINIUM (domain) → GENUS (category) → SPECIES (specifier) → CORPUS (body) → FINIS (terminator). Visual glyph families correlate with their slot far more than chance allows (p = 0.0007). This is the CLAVIS CODICIS — the syntactic key.

On the "meaningless hoax" hypothesis. Several authors have argued that the manuscript is gibberish generated by a 15th-century device. We implemented every published candidate and measured its weighted Euclidean distance d to the Voynich fingerprint:

• Cardan grille (Rugg 2004; Rugg & Taylor 2017) — table-based shuffler: d = 4.485 (worst of all 11 models tested); over-regular and over-predictable.
• Self-citation algorithm (Timm & Schinner 2020, 2024) — scribe copies and modifies earlier words: d = 1.356; produces a flat curve (bounce 0.120 vs Voynich 0.813).
• Polygraphia III (Hermes 2022) — Trithemius-style polygraphic substitution.
• Naibbe verbose homophonic cipher (Greshko 2025) — the closest of any published model, yet still d = 1.028 (more than 2× the distance of our SilPart model, d = 0.445), with zero positional MI (vs 0.658 for the Voynich).

None of the four reproduces the full fingerprint. The two pre-radiocarbon "modern forgery" candidates (Wilfrid Voynich himself in 1912; the Elizabethan Kelley/Dee circle) are independently excluded by the parchment's C14 date of 1404–1438.

What this means. The Voynich is not a meaningless hoax, not a natural language, and not a classical cipher. It is an artificial categorial code: each word is a structured address inside a classification system, like a library call number. We have recovered the syntax of that system; recovering the semantics still requires the original key book to surface in a library somewhere — which is the next stage of the project.

A note on the CLAVIS CODICIS — what it is and what it is not. The name means "Key of the Codex" in Latin, and the five slot labels (DOMINIUM, GENUS, SPECIES, CORPUS, FINIS) are also in Latin. This is a deliberate choice: they are descriptive scholarly labels for positions, not translations of any glyph. Latin matches both the medieval intellectual environment of the manuscript and Caramuel's Latin formalisation of cifras ineffabiles; using everyday English or Spanish words for the slots could be misread as a proposed meaning. The CLAVIS CODICIS is a syntactic key, not a semantic one. It tells you which glyph can occupy which position in a Voynich word, not what any glyph means. Recovering it is comparable to learning that English sentences follow Subject–Verb–Object without learning what "cat" or "runs" denotes: we now have the grammar of the code, but the dictionary that maps each slot value to a real-world referent (a plant, a star, a pharmaceutical ingredient) remains lost. This work is not a decipherment of the Voynich Manuscript. It is the most precise structural description of its encoding produced to date — the necessary scaffolding that any future decipherment will have to satisfy.

For the technically inclined: jump to Key results; the full evidence is in the 11 documentation parts, the 61 notebooks below, and the four peer-targeted papers — Paper 1: Negative result · Paper 2: Two-tier encoding · Paper 3: Venus Ring of f57v · Paper 4: Positional Role Grammar / CLAVIS CODICIS.

Español

El Manuscrito Voynich es un libro ilustrado de 240 páginas escrito hacia 1404–1438 en un alfabeto que nadie más ha usado jamás. Durante 600 años, eruditos, criptógrafos y aficionados han intentado leerlo, y todos han fracasado. Este proyecto es un intento sistemático por vía computacional — y un informe honesto de dónde se rompe el texto.

Lo que hicimos. Tratamos cada hipótesis estándar como una predicción comprobable y las ejecutamos todas: que sea una lengua natural disfrazada (hebreo, arameo, árabe, hebreo tibbónida, judeo-árabe, ge'ez), que sea un cifrado clásico (sustitución, polialfabético, transposición, nomenclátor), que sea galimatías, que sea una lengua construida. Diecinueve modelos de sustitución, cinco lenguas semíticas, tres tipos de sistema de escritura — todos chocan contra el mismo muro.

Lo que encontramos.

• El texto es real. Posee una estructura interna rígida que ningún galimatías aleatorio reproduce; en concreto, los glifos están fijados por posición dentro de la palabra a un nivel el doble de fuerte que cualquier lengua natural que medimos.
• No es una lengua natural escondida. Todos los modelos que intentan asignar letras de un alfabeto real a los glifos se estancan en el mismo techo: unas pocas raíces válidas y, como máximo, ~68 % de bigramas válidos.
• Es un código posicional. Lo que importa es la posición del glifo en la palabra, no el "valor de letra" del glifo. Este patrón coincide con una categoría teórica del siglo XVII — la cifra ineffabilis / pasigrafía filosófica de Caramuel — cuyas raíces se remontan a Ramon Llull y a la combinatoria medieval aristotélico-cabalística.
• Un folio es especial. El folio f57v ("el anillo de Venus") contiene cinco glifos que no aparecen en ningún otro lugar del manuscrito — un subalfabeto privado cuya iconografía coincide con los karacteres descritos en el tratado astrológico medieval Picatrix.
• La gramática puede reconstruirse. Cada palabra Voynich sigue una plantilla fija de 5 ranuras: DOMINIUM (dominio) → GENUS (categoría) → SPECIES (especificador) → CORPUS (cuerpo) → FINIS (terminador). Las familias visuales de glifos se correlacionan con su ranura mucho más de lo que el azar permite (p = 0,0007). Esta es la CLAVIS CODICIS — la llave sintáctica.

Sobre la hipótesis del "fraude sin sentido". Varios autores han defendido que el manuscrito es galimatías generado por un dispositivo del siglo XV. Implementamos cada candidato publicado y medimos su distancia euclídea ponderada d a la huella estadística del Voynich:

• Rejilla de Cardano (Rugg 2004; Rugg & Taylor 2017) — barajador basado en tabla: d = 4,485 (la peor de los 11 modelos testados); demasiado regular y demasiado predecible.
• Algoritmo de autocitación (Timm & Schinner 2020, 2024) — el escriba copia y modifica palabras anteriores: d = 1,356; produce una curva plana (bounce 0,120 frente a 0,813 del Voynich).
• Polygraphia III (Hermes 2022) — sustitución poligráfica al estilo de Tritemio.
• Cifra homofónica detallada Naibbe (Greshko 2025) — la más cercana de toda la literatura, pero aún a d = 1,028 (más del doble que nuestro modelo SilPart, d = 0,445), con MI posicional nulo (frente a 0,658 del Voynich).

Ninguno de los cuatro reproduce la huella completa. Los dos candidatos a "falsificación moderna" anteriores al carbono-14 (el propio Wilfrid Voynich en 1912; el círculo isabelino de Kelley/Dee) quedan descartados de forma independiente por la datación C14 del pergamino: 1404–1438.

Lo que esto significa. El Voynich no es un fraude sin sentido, no es una lengua natural y no es un cifrado clásico. Es un código categorial artificial: cada palabra es una dirección estructurada dentro de un sistema de clasificación, como una signatura de biblioteca. Hemos recuperado la sintaxis de ese sistema; recuperar la semántica todavía requiere que el libro-llave original aparezca en alguna biblioteca — esa es la siguiente etapa del proyecto.

Una nota sobre la CLAVIS CODICIS — qué es y qué no es. El nombre significa "Llave del Códice" en latín, y las cinco etiquetas de ranura (DOMINIUM, GENUS, SPECIES, CORPUS, FINIS) están también en latín. Es una elección deliberada: son etiquetas académicas descriptivas de posiciones, no traducciones de ningún glifo. El latín se ajusta tanto al ambiente intelectual medieval del manuscrito como a la formalización latina de las cifras ineffabiles por Caramuel; usar palabras cotidianas en español o inglés para nombrar las ranuras podría malinterpretarse como una propuesta de significado. La CLAVIS CODICIS es una llave sintáctica, no semántica. Indica qué glifo puede ocupar qué posición en una palabra Voynich, no qué significa cada glifo. Recuperarla equivale a saber que las frases en español siguen Sujeto–Verbo–Objeto sin saber qué denotan "gato" o "corre": tenemos ya la gramática del código, pero el diccionario que asigna a cada valor de ranura un referente real (una planta, una estrella, un ingrediente farmacéutico) sigue perdido. Este trabajo no es un descifrado del Manuscrito Voynich. Es la descripción estructural más precisa de su cifrado producida hasta la fecha — el andamiaje necesario que cualquier descifrado futuro deberá satisfacer.

Para lectores técnicos: ir a Key results; la evidencia completa está en las 11 partes de documentación, los 61 notebooks listados más abajo, y los cuatro artículos académicos — Paper 1: Resultado negativo · Paper 2: Codificación de dos niveles · Paper 3: El anillo de Venus de f57v · Paper 4: Gramática de roles posicionales / CLAVIS CODICIS.

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Published archives (Zenodo)

Phase	Contents	DOI
Phase 1	Papers 1 + 2 (negative result + two-tier encoding) and notebooks 01–48	10.5281/zenodo.19188265
Phase 2	Papers 3 + 4 (Venus Ring of f57v + Positional Role Grammar) and notebooks 67–78 + 74b	10.5281/zenodo.19546774

Theoretical framework

The Voynich Manuscript is read here as a philosophical pasigraphy / cifra ineffabilis (in the sense that Caramuel formalised in 1665, drawing on older Lullian, Aristotelian and Kabbalistic traditions): the glyphs encode categorical properties through their position in the word, not by substituting for letters of a natural language. See caramuel_parallel.md for the full historical and structural justification, and Martínez Gavilán 2025 (10.5281/zenodo.17961147).

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Repository Structure

.
├── corpus/                           # Voynich corpus (STA1 2.0 + EVA)
├── voynich_part[1-11].md             # Documentation in 11 parts (Spanish)
├── voynich_part[1-11]_en.md          # English translations
├── caramuel_parallel.md              # Theoretical framework (pasigraphy / cifra ineffabilis)
├── *.ipynb                           # 61 Jupyter notebooks
├── resultados/                       # 35 JSON result files (one per executed notebook)
├── images/                           # Figures generated by the notebooks
├── pages/                            # Voynich folio facsimile crops used as inputs
├── tools/                            # Auxiliary scripts (circular text unwrap, etc.)
├── paper/                            # Paper 1 — Negative result (LaTeX, 3 wrappers + supplements)
├── paper2/                           # Paper 2 — Two-tier encoding (LaTeX, 3 wrappers)
├── paper3/                           # Paper 3 — Venus Ring of f57v (LaTeX)
├── paper4/                           # Paper 4 — Positional Role Grammar (LaTeX)
├── .gitignore
└── README.md

Documentation

The research is organised in 11 parts (36 chapters), bilingual:

Part	EN (AI translation)	ES	Chapters	Content
I	part1	part1	1–3	Historical context, state of the art, STA1 2.0 corpus
II	part2	part2	4–8	Foundations: Shannon entropy, permutation tests, chi-squared, Markov, Transformers
III	part3	part3	9–15	7 tests on 8 corpora, multilingual controls, 11 generative models, scorecard
IV	part4	part4	16	Syllabic segmentation: 2,923 types, onset/nucleus/coda classification, harmony
V	part5	part5	17	Bayesian syllabic decipherment: 5 languages, Hebrew #1, multi-chain MCMC
VI	part6	part6	18	Compositional decipherment: glyph-to-character, Hebrew #1, 11.7 pt gap
VII	part7	part7	19–20	Validation (5 tests: degenerate) + constrained EM with grammar anchors
VIII	part8	part8	21–22	Semantic, homophonic positional, Bayesian with Aramaic (6 languages)
IX	part9	part9	23–27	Neural LM, lexical scoring, Neural v2 multi-seed, syllabic-positional, Aramaic
X	part10	part10	28–35	Allographs, syl-homophonic, registers, syl-to-syl, nucleus-only, partial NULL, EVA, morphological, cross-linguistic, C/V, zodiac cribs, cipher diagnostics, nomenclator
XI	part11	part11	35.11–36	Two-tier encoding, distributional clustering, recipe code simulation, structural decoding, TP robustness, final synthesis

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Notebooks (61)

Block A — Statistical fingerprint and generative models (01–05)

Notebook	Description	Part
01_statistical_fingerprint.ipynb	STA1 2.0 parser, entropy, positional MI, Markov, embeddings	III
02_permutation_bootstrap.ipynb	Permutation tests, bootstrap, folio-level holdout	III
03_entropy_spectral.ipynb	Conditional entropy, spectral gap, JSD between sections	III
04_multilingual_controls.ipynb	6 languages + 2 ciphers as controls	III
05_generative_models.ipynb	11 generative models (7 novel + 4 from the literature)	III

Block B — Decipherment battery: 19 models (06–22, 24–26, 33–35)

#	Notebook	Model	Scorecard	Key result	Ch.
1	06_bayesian_syllabic.ipynb	Bayesian syllabic	–	Hebrew #1 (-35.64)	17
2	07_compositional.ipynb	Compositional SilPart	1+/1±/3−	Degenerate	18
3	09_constrained_em.ipynb	Constrained EM	–	100 roots, n-gram 5%	20
4	11_homophonic.ipynb	Homophonic positional	2+/2±/2−	w_homo inert	22
5	12_neural_lm.ipynb	Neural LSTM T=3	4+/0±/1−	N-gram 38%, 1 root	23
6	13_lexical_scoring.ipynb	Lexical S_root	2-3+/1-2±/1−	Intrinsic trade-off	24
7	14_neural_v2.ipynb	Neural v2 multi-seed	4+/0±/1−	N-gram 68% (record)	25
8	15_syllabic_positional.ipynb	Syllabic-positional	4+/2±/0−	3 tables, R-hat 92%	26
9	16_syllabic_aramaic.ipynb	Syllabic Aramaic	4+/2±/0−	Identical to Hebrew	27
10	17_allograph.ipynb	Positional allographs	4+/0±/2−	Discarded	28
11	18_syllabic_homophonic.ipynb	Syllabic homophonic	3+/1±/2−	Discarded	29
12	20_syllable_to_syllable.ipynb	Syllable-to-syllable	2+/1±/2−	Discarded	–
13	21_nucleus_only.ipynb	Nucleus-only	4+/0±/1−	N-gram 100%*, 2 roots	–
14	24_neural_v2_eva.ipynb	Neural v2 (EVA)	2+/0±/3−	N-gram 0%, 0 roots	–
15	25_morphological.ipynb	Morphological subst.	4+/1±/1−	N-gram 16%, 0 roots	–
16	26_morphological_zohar.ipynb	Morph. Zohar	3+/0±/3−	N-gram 0%, 1 root	–
17	33_tibbonid_hebrew.ipynb	Tibbonid Hebrew	3+/1±/1−	N-gram 13%, 3 roots	35
18	34_judeo_arabic.ipynb	Judeo-Arabic (proxy)	2+/1±/2−	N-gram 12%, 1 root	35
19	35_geez.ipynb	Ge'ez (Ethiopic)	1+/0±/3−	N-gram 0%, ratio ~1:1 fails	35

Block C — Auxiliary, robustness, ablations (08, 10, 19, 22, 23, 27)

Notebook	Description	Ch.
08_validation.ipynb	Compositional validation (5 tests)	19
10_semantic.ipynb	Semantic analysis (chi-squared, correspondences)	21
19_registers.ipynb	3 Hebrew registers (Torah/Mishnah/Zohar) — Discarded	30
22_partial_null.ipynb	Partial NULL threshold sweep	–
23_transcription_robustness.ipynb	Transcription robustness: STA1 2.0 vs EVA	–
27_cv_constraint.ipynb	C/V role constraint ablation — Discarded	–

Block D — Cipher diagnostics, cribs, nomenclator (28–32)

Notebook	Description	Ch.
28_zodiac_cribs.ipynb	Zodiac page crib extraction — Not significant	–
29_cipher_diagnostics.ipynb	IC, Kasiski, bigram, transposition diagnostics	–
30_nomenclator_separation.ipynb	Nomenclator glyph-level separation — Discarded	–
31_word_nomenclator.ipynb	Nomenclator word-level separation — Discarded	–
32_enochian_comparison.ipynb	Enochian constructed-language comparison	–

Block E — Two-tier encoding and code anatomy (36–48)

Notebook	Description	Ch.
36_silpart_structure.ipynb	SilPart deep structure: two-tier encoding analysis	35
37_distributional_clustering.ipynb	Distributional clustering of onsets/codas	35
38_constructed_languages.ipynb	Comparison with Esperanto, Enochian, Lingua Ignota	35
39_herbal_onset_analysis.ipynb	Herbal section: onset clusters vs plant categories	35
40_recipe_code_simulation.ipynb	Medieval recipe code simulation	35
41_structural_decoding.ipynb	Code dictionary skeleton	35
42_tp_threshold_robustness.ipynb	TP threshold robustness test	35
43_intra_folio_analysis.ipynb	Intra-folio positional analysis: 3-zone entry structure	35
44_code_anatomy.ipynb	Code anatomy: identifiers, selectivity matrix, information capacity	35
45_structural_reading.ipynb	Word-by-word entry parsing	35
46_vocabulary_network.ipynb	Vocabulary network: folio communities from shared T2 words	35
47_sta_metadata_analysis.ipynb	STA1 metadata: $I type, Currier language, writing hand	35
48_selectivity_and_registers.ipynb	Selectivity matrix, register lexicons, isolated folios	35

Block F — Zodiac decipherment (67–73) — supports Paper 3

Notebook	Description
67_zodiac_quire_reconstruction.ipynb	Quire reconstruction: zodiac block as a calendar
68_zodiac_label_analysis.ipynb	Deep analysis of nymph labels
69_zodiac_consolidated.ipynb	Consolidated zodiac model
70_zodiac_astrological_encoding.ipynb	Astrological encoding: 30 degrees per sign
71_zodiac_definitive.ipynb	Definitive model: atom positions 2/3/4 encode season/fertility/sign type
72_zodiac_visual_catalog.ipynb	Visual catalog: tubes/dress/crowns correlate with season
73_zodiac_Q1Q2_heidelberg.ipynb	Q1/Q2 quire mystery + Heidelberg Astrolabium Planum parallel

Block G — f57v private subalphabet (74, 74b) — Paper 3 core

Notebook	Description
74_f57v_private_subalphabet.ipynb	5 glyphs exclusive to f57v + 3 strongly enriched (Eb, Ja, X1); chance ≈ 10⁻²⁶
74b_f57v_graphic_vocabulary_quantitative.ipynb	Quantitative graphic vocabulary; cosmological-iconography robustness check

Block H — Positional role grammar and structural dictionary (75–78) — Paper 4

Notebook	Description
75_family_position_correlation.ipynb	Visual glyph families correlate with word position (z = -3.38, p = 0.0007)
76_role_grammar_and_sections.ipynb	6 functional roles (OPENER → ENCODER 63.5%); section classifier 66.4%
77_minimal_dictionary.ipynb	Minimal structural dictionary export
78_key_book_visualization.ipynb	CLAVIS CODICIS: 5-slot schema (DOMINIUM / GENUS / SPECIES / CORPUS / FINIS)

Tools

File	Description
tools/circular_text_unwrap.ipynb	Polar→linear unwrap of f57v's circular text rings

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Results files (resultados/, 35 JSON + 2 CSV)

File	Source notebook
alchemical_herbal_crossref_resultados.json	Alchemical herbal cross-reference
botanical_anchor_validation_resultados.json	Botanical anchor validation
botanical_candidates_resultados.json	Botanical candidates analysis
color_channel_comparison_resultados.json	Visual herbal: colour channel comparison
contour_herbal_comparison_resultados.json	Visual herbal: contour comparison
cropped_herbal_comparison_resultados.json	Visual herbal: cropped comparison
cross_validation_ntizar_resultados.json	Cross-validation (Ntizar collaborator)
distributional_clustering_resultados.json	Distributional clustering of onsets/codas
dual_structure_resultados.json	Dual structure analysis
green_roots_comparison_resultados.json	Visual herbal: green-root comparison
holdout_validation_ntizar_resultados.json	Hold-out validation (Ntizar)
index_reconstruction_resultados.json	Index reconstruction
positional_structure_resultados.json	Positional structure analysis
rare_first_reconstruction_resultados.json	Rare-first reconstruction
rtl_hypothesis_resultados.json	RTL (right-to-left) hypothesis test
selectivity_registers_resultados.json	Selectivity matrix and register lexicons
semitic_root_parallel_resultados.json	Semitic root parallel
shape_herbal_comparison_resultados.json	Visual herbal: shape comparison
silpart_stem_extraction_resultados.json	SilPart stem extraction
specificity_proportions_tracking_resultados.json	Specificity proportions tracking
sta_metadata_resultados.json	STA1 metadata analysis
suffix_function_resultados.json	Suffix function analysis
suffix_transitions_wellformed_resultados.json	Suffix transitions and well-formedness
tzeruf_structural_resultados.json	Tzeruf structural test
visual_herbal_comparison_resultados.json	Visual herbal comparison (CLIP)
visual_comparison_summary.json	Visual comparison summary
vocabulary_network_resultados.json	Vocabulary network
zodiac_astrological_encoding_resultados.json	Zodiac astrological encoding
zodiac_consolidated_resultados.json	Zodiac consolidated model
zodiac_definitive_resultados.json	Zodiac definitive model (nb 71)
zodiac_label_analysis_resultados.json	Zodiac label analysis
zodiac_q1q2_heidelberg_resultados.json	Q1/Q2 + Heidelberg parallel
zodiac_quire_reconstruction_resultados.json	Zodiac quire reconstruction
zodiac_visual_catalog_resultados.json	Zodiac visual catalog
botanical_candidates_for_david.csv	Botanical candidate shortlist
visual_comparison_checklist.csv	Visual comparison checklist

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Key results

Statistical fingerprint (Parts I–III)

• U-shaped entropy curve (bounce = 0.813 bits): unique among 6 languages + 2 ciphers. Character-level conditional entropy curve, distinct from the word-level distributional U reported by Montemurro & Zanette (2013).
• Positional MI of 0.658 bits (p = 0.0000 by permutation test): 2× the highest language (Hebrew, 0.311). Quantification of the qualitative observation by Stolfi (1997).
• Inter-folio stability r = 0.9999.
• Spectral gap (0.541) clusters with agglutinative languages (Turkish, Finnish), not with Semitic.
• Of 11 generative models, only SilPart (d = 0.445) — formalising Stolfi's "crust-mantle-core" — reproduces the fingerprint; the best from the literature (Naibbe/Greshko 2025, d = 1.028) is over twice as distant.

Syllabic segmentation (Part IV)

• 2,923 syllabic types (~200 functional): onset (171), nucleus (54), coda (90).
• MI does not amplify glyph-to-syllable (0.92×, vs ~4× in Turkish/Finnish): glyphs already operate at a high encoding level.

Decipherment: language ranking (Parts V–VIII)

• Hebrew #1 in all rankings (syllabic: -35.64, compositional: -39.71). Compatible with Hauer & Kondrak (2016), who first reported Hebrew as best-fit using a different (anagram-based) methodology.
• Hebrew ~ Aramaic: gap 0.27 nats (bootstrap 95% CI spans zero) — "NW Semitic biblical" as a single functional category.
• Semitic vs. non-Semitic gap: 2.9–11.7 points.

19 decipherment models — convergent ceiling (Part IX)

#	Model	Target	|Σ|/|A|	N-gram	Roots	R-hat	Scorecard
1	Compositional	Hebrew	6.1	24%	6	59%	1+/1±/3−
2	Constrained EM	Hebrew	6.1	5%	100	40%	–
3	Homophonic	Hebrew	6.1	28%	–	68%	2+/2±/2−
5	Neural v1	Hebrew	6.1	38%	1	70%	4+/0±/1−
6	Lexical S_root	Hebrew	6.1	12%	3-4	67-71%	2-3+/1-2±/1−
7	Neural v2	Hebrew	6.1	68%	3	71%	4+/0±/1−
8	Syl-positional	Hebrew	6.1	14%	5	92%	4+/2±/0−
9	Syl-positional	Aramaic	6.1	6%	5	90%	4+/2±/0−
10	Allograph	Hebrew	5.4	23%	4	54%	4+/0±/2−
11	Syl-homophonic	Hebrew	6.1	22%	1	82%	3+/1±/2−
12	Syl-to-syl	Hebrew	0.68	0.1%	25*	4%	2+/1±/2−
13	Nucleus-only	Hebrew	4.4	100%**	2	95.8%	4+/0±/1−
14	Neural v2 EVA	Hebrew	1.26	0%	0	66.7%	2+/0±/3−
15	Morphological	Hebrew	6.1	16%	0	84.3%	4+/1±/1−
16	Morph. Zohar	Aramaic	6.1	0%	1	97.1%	3+/0±/3−
17	Tibbonid	Hebrew (philos.)	6.1	13%	3	54.2%	3+/1±/1−
18	Judeo-Arabic	Arabic (proxy)	7.5	12%	1	65.5%	2+/1±/2−
19	Ge'ez	Ethiopic	0.88	0%	–	80.5%	1+/0±/3−

* Spurious: decoded words average 2.42 chars. ** Inflated: nucleus-only words average 2.22 glyphs. Model 19 is the first test at ratio ~1:1 — worst n-gram despite best ratio, proving the ceiling is structural.

Two-tier encoding (Part XI, §35.11–35.15) — Paper 2

• Two-tier structure: 48.3% Tier-1 (structural markers) and 51.7% Tier-2 (content glyphs), separated by transition probability profiles.
• Extreme combinatorial restriction: only 6.7% of possible Tier-2 bigrams are attested — 93.3% of the combinatorial space is forbidden.
• Onset/coda asymmetry: ratio 1.95.
• No natural language match: comparison with Hebrew, Latin, Arabic, Turkish, Finnish shows no comparable two-tier separation; Esperanto (constructed) is the closest match.
• Herbal onsets do not encode plant categories (p = 0.336), but section-level encoding is highly significant (p < 10⁻⁸⁴).
• Recipe code simulation: constrained code with p_valid = 0.08 matches the 6.7% utilisation.
• Structural inventory: 125 classified elements (20 markers, 83 section headers, 21 modifiers) with regular T1–T2 alternation grammar.
• Robust across thresholds: utilisation 6–12% and onset/coda ratio > 1 hold at 7/8 TP thresholds (P5–P40).

Zodiac block decipherment (notebooks 67–73)

• The zodiac quires reconstruct as a calendar (12 signs × 30 degree-positions).
• Atoms in word positions 2 / 3 / 4 of nymph labels encode season / fertility / sign type respectively (notebook 71 — strongest empirical finding of the project).
• Visual–textual coherence: tubes, dress and crowns of the nymphs correlate with season (notebook 72).
• The closest documented pre-1438 structural parallel is the Heidelberg Astrolabium Planum (Pietro d'Abano, c. 1300); the Q1/Q2 quire question remains open (notebook 73).

f57v private subalphabet (notebooks 74, 74b) — Paper 3

• Folio f57v contains 5 glyphs exclusive to that single folio (X2, Xd, Xf, Pc, Ea, all 100% in f57v) plus 3 strongly enriched (Eb, Ja, X1). Enrichment factors 60–367×; probability of chance concentration ≈ 10⁻²⁶.
• Only folio in the 224-folio corpus with this signature; robustness check against 7,134 comparison atoms across the cosmological/astronomical iconographic family (ff. 67–70) finds zero occurrences of the seven strongest subalphabet glyphs.
• Direct verification against Cracow Jagiellonian MS 793 (Picatrix Latinus, 1471–1474) yields three iconographic correspondences with f57v's central solar disc and shield sigils.
• Interpretation: the Voynich is an independent witness of the medieval astrological-talismanic tradition codified by Picatrix Latinus, preserving the karacteres alphabet more completely than MS 793 itself.

Positional role grammar and structural dictionary (notebooks 75–78) — Paper 4

• Form ↔ function correlation: visual glyph families concentrate in specific word positions far more than chance predicts (z = -3.38, p = 0.0007).
• 6 functional roles (OPENER, ENCODER, CONNECTOR, BODY, SCAFFOLD, CLOSER) cover 99.5 % of tokens; the grammar is strongly directional (OPENER → ENCODER = 63.5 % of first→second transitions); some role pairs are effectively forbidden (O/E < 0.3).
• A leave-one-out folio classifier on role proportions alone reaches 66.4 % accuracy across 5 sections (chance baseline 27 %).
• CLAVIS CODICIS — 5-slot schema: DOMINIUM (pos. 1), GENUS (pos. 2), SPECIES (pos. 3, highest entropy 4.09 bits), CORPUS (pos. 4), FINIS (pos. 5–6). Each slot has a closed inventory with measurable section specificity (JSD 0.186–0.226). Exported as voynich_structural_dictionary.json (kept private; figure available in 78_key_book_visualization.ipynb).
• The recovered schema is the syntax of the lost key book; content access still requires the key book itself.

Conclusions

Finding	Evidence
Real positional structure	MI 2× the highest language; 73% of glyphs position-locked
Unique U-shape	0/6 languages + 0/2 ciphers reproduce it
Compatible language: NW Semitic	Hebrew #1 across all rankings; Aramaic indistinguishable
Best substitution model: Neural v2	68% n-gram (record), single glyph-to-character table
Structural ceiling	~2–5 roots and ~68% n-gram: 19 models converge on the same limit
Position ≠ meaning	Position affects glyph selection, not its value
Transcription-independent	MI_pos, spectral gap, inter-folio stable under EVA; bounce is STA1-specific
EVA decipherment	|Σ|/|A| = 1.26 (solvable range) yet 0% n-gram: barrier is encoding, not alphabet size
Discarded hypotheses	Allographic, syllabic homophonic, alternative register, positional polyphony, syllable-to-syllable, nucleus-only, morphological substitution, morphological (Zohar/Aramaic), EVA substitution, abjad mismatch (C/V), polyalphabetic, polygraphic, transposition, nomenclator (glyph + word level), Tibbonid Hebrew, Judeo-Arabic, Ge'ez
Cipher-type paradox	All 4 diagnostics say monoalphabetic/natural language, yet 19 mono models fail
Two-tier encoding	48.3% T1 + 51.7% T2; only 6.7% utilisation; onset/coda ratio 1.95; no natural language reproduces this
Zodiac decipherment	Atom positions 2/3/4 encode season/fertility/sign type; visual–textual coherence
f57v private subalphabet	5 exclusive + 3 enriched glyphs, chance ≈ 10⁻²⁶; iconographic match with Picatrix MS 793
Role grammar	6 roles, OPENER→ENCODER 63.5%; section classifier 66.4% (chance 27%)
CLAVIS CODICIS	5-slot positional schema (DOMINIUM/GENUS/SPECIES/CORPUS/FINIS) — syntax of the lost key book
Theoretical framework	Philosophical pasigraphy / cifra ineffabilis (Caramuel 1665, formally documenting older Lullian/Aristotelian/Kabbalistic traditions); see caramuel_parallel.md

Multilingual controls

Corpus	Family	Bounce	Gap delta	MI_pos	MI_big
Voynich	–	0.813	0.541	0.658	1.681
Latin	Indo-European	0.000	0.658	0.267	1.082
Caesar	Monoalph. cipher	0.000	0.658	0.267	1.082
Vigenère	Polyalph. cipher	0.000	0.855	0.053	0.445
Hebrew	Semitic	0.000	0.812	0.311	0.607
Arabic	Semitic	0.000	0.798	0.234	0.749
Turkish	Agglutinative	0.000	0.509	0.151	0.835
Finnish	Agglutinative	0.000	0.577	0.205	0.652

---

Getting started

Prerequisites

• Python 3.12+
• Git
• CUDA-capable GPU (optional, recommended for notebooks 12–18 which train neural language models)
• ~2 GB disk space (including PyTorch)

Installation

1. Clone the repository

git clone https://github.com/cesarjz/Voynich.git
cd Voynich

2. Create a virtual environment

python3 -m venv .venv
source .venv/bin/activate   # Linux / macOS
# .venv\Scripts\activate    # Windows

3. Install dependencies (no requirements.txt is shipped — the canonical set is below):

pip install numpy pandas scipy scikit-learn matplotlib seaborn networkx tqdm requests
pip install torch                       # CUDA build by default; for CPU-only:
# pip install torch --index-url https://download.pytorch.org/whl/cpu
pip install transformers                # only needed for CLIP-based visual notebooks (65–66, in private archive)
pip install ipykernel nbconvert
python -m ipykernel install --user --name voynich --display-name "Voynich (venv)"

Running the notebooks

Interactive:

jupyter notebook   # or: jupyter lab

Select the "Voynich (venv)" kernel when opening a notebook.

Batch (single notebook):

jupyter nbconvert --to notebook --execute --inplace \
  --ExecutePreprocessor.timeout=-1 \
  --ExecutePreprocessor.allow_errors=True \
  NOTEBOOK.ipynb

Batch (all notebooks):

for nb in *.ipynb; do
  echo "=== $nb ==="
  jupyter nbconvert --to notebook --execute --inplace \
    --ExecutePreprocessor.timeout=-1 \
    --ExecutePreprocessor.allow_errors=True \
    "$nb"
done

Execution time: notebooks 01–05 run in minutes. Decipherment models (06–18, 33–35) can take 30 minutes to several hours each due to multi-seed EM and MCMC. Notebooks 19–48 typically run in 10–60 minutes. Zodiac and role-grammar notebooks (67–78) run in seconds to minutes.

Execution order

Notebooks are designed to be independently executable — each one loads its own data and trains its own models. There are no cross-notebook dependencies. The natural reading order follows the numbering.

External data

The Voynich corpus (corpus/voynich_sta.txt and the EVA companion) is included. Hebrew, Aramaic and other language corpora are downloaded automatically at runtime from Sefaria-Export (requires internet on first run).

---

Papers (LaTeX)

All four papers compile to PDF from sources in this repository.

Paper 1 — Negative result (paper/)

Wrappers, plus two supplementary documents:

paper/
├── voynich_paper.tex            # wrapper
├── voynich_body.tex             # Shared body
├── voynich_abstract.tex         # Shared abstract
├── voynich_keywords.tex         # Shared keywords
├── voynich_paper.bib            # Bibliography
├── supplementary_A_conceptual_bridge.tex
├── supplementary_B_causal_funnel.tex
├── arxiv/voynich_arxiv.tex      # arXiv wrapper (A4, 11 pt, standard article)
├── ebook/voynich_ebook.tex      # eBook wrapper (A5, 14 pt, e-readers)
└── references/                  # Bibliography checklist + downloaded reference PDFs

Paper 2 — Two-tier encoding (paper2/)

Cryptologia target with arXiv and eBook wrappers:

paper2/
├── twotier_paper.tex            # wrapper
├── twotier_body.tex
├── twotier_abstract.tex
├── twotier_keywords.tex
├── twotier_paper.bib
├── arxiv/twotier_arxiv.tex
└── ebook/twotier_ebook.tex

Paper 3 — Venus Ring of f57v (paper3/)

paper3/
├── venusring_paper.tex
├── venusring_body.tex
├── venusring_abstract.tex
├── venusring_keywords.tex
├── venusring_paper.bib
└── venusring_paper.pdf          # Compiled output included

Paper 4 — Positional Role Grammar / CLAVIS CODICIS (paper4/)

paper4/
├── rolegrammar_paper.tex
├── rolegrammar_body.tex
├── rolegrammar_abstract.tex
├── rolegrammar_keywords.tex
├── rolegrammar_paper.bib
└── rolegrammar_paper.pdf        # Compiled output included

Compiling

All four papers follow the same compilation pattern. Edit the body / abstract / keywords and recompile:

# Paper 1 
cd paper/arxiv && pdflatex voynich_arxiv && bibtex voynich_arxiv && pdflatex voynich_arxiv && pdflatex voynich_arxiv

# Paper 1 — eBook (A5, 14 pt)
cd paper/ebook && pdflatex voynich_ebook && bibtex voynich_ebook && pdflatex voynich_ebook && pdflatex voynich_ebook

# Paper 2 — normal or eBook
cd paper2/arxiv && pdflatex twotier_arxiv && bibtex twotier_arxiv && pdflatex twotier_arxiv && pdflatex twotier_arxiv
cd paper2/ebook && pdflatex twotier_ebook && bibtex twotier_ebook && pdflatex twotier_ebook && pdflatex twotier_ebook

# Paper 3 — Venus Ring of f57v
cd paper3 && pdflatex venusring_paper && bibtex venusring_paper && pdflatex venusring_paper && pdflatex venusring_paper

# Paper 4 — Role Grammar
cd paper4 && pdflatex rolegrammar_paper && bibtex rolegrammar_paper && pdflatex rolegrammar_paper && pdflatex rolegrammar_paper

# Paper 1 — supplementary documents (standalone)
cd paper && pdflatex supplementary_A_conceptual_bridge && pdflatex supplementary_A_conceptual_bridge
cd paper && pdflatex supplementary_B_causal_funnel && pdflatex supplementary_B_causal_funnel

---

Dependencies

Package	Purpose
matplotlib	Visualization
networkx	Graph analysis (embedding networks, vocabulary network)
numpy	Numerical computation
pandas	Data manipulation
requests	Corpus download (Sefaria API)
scikit-learn	PCA, clustering, cosine similarity
scipy	Statistical tests, optimization
seaborn	Statistical visualization
torch	Neural language models (LSTM)
tqdm	Progress bars

Licence

Independent academic research. The Voynich corpus (STA1 2.0 and EVA) is in the public domain. Hebrew and Aramaic corpora from Sefaria-Export (CC-BY-SA).

Citing this work

If you use this material, please cite the corresponding Zenodo archive:

Jimenez Zapata, C. (2026). Computational Analysis and Two-Tier Encoding of the
Voynich Manuscript: Code, Data, and Papers (1.0) [Data set]. Zenodo.
https://doi.org/10.5281/zenodo.19188265

Jimenez Zapata, C. (2026). Voynich Manuscript Phase 2: Zodiac Decipherment,
Talismanic Tradition (Picatrix), and Structural Dictionary Reconstruction —
Code, Data, and Papers [Data set]. Zenodo. https://doi.org/10.5281/zenodo.19546774