4-slot FSM and procedural gemination in the ZL corpus (Python)

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Hello everyone,

I would like to share the methodology and empirical findings of a quantitative study conducted on the Zandbergen-Landini transcription corpus (ZL3b-n.txt, 5,316 lines, 33,645 tokens). Rather than attempting an ad-hoc translation of isolated folios or asserting arbitrary linguistic substitutions, this study examines whether the lexical and syntactic layers of MS 408 can be formally modeled as a deterministic positional state machine, evaluates sequential transition entropy, and quantifies section-dependent operational constraints.

All analyses were implemented in Python and are fully reproducible on the raw ZL corpus. The complete script pipeline is attached to this post.

1. The 4-Slot Morphotactic FSM Model

Testing positional slot constraints indicates that Voynichese word tokens are predominantly generated by a strict, left-to-right positional finite-state grammar rather than natural inflectional morphology:

Token = [S0: Prefix] + [S1: Gallows Selector] + [S2: Kernel/Core] + [S3: Terminal/Minims]

Slot Inventory:

• S0 (34 Prefixes): qok-, qot-, qop-, qo-, che-, cho-, she-, sho-, da-, d-, sa-, ol-, ok-, ot-, etc.
  
• S1 (9 Gallows / Ligatures): k, t, p, f, cth, ckh, cph, cfh, d.
  
• S2 (35 Kernels): chol, chor, ee, al, ar, eol, ai, od, etc.
  
• S3 (23 Terminals / Minims): -in, -iin, -iiin, -iiiin, -edy, -eedy, -y, -ey, -al, -ar, etc.
  

Quantitative Parameters:

• Corpus Coverage: The 4-slot automaton successfully parses 84.01% of all lexical tokens across 5,316 lines of text without requiring external dictionary lookups or fuzzy stems.
  
• Information Density: The resulting state distribution yields an empirical word entropy of H = 10.47 bits/token and a combinatorial redundancy of R = 18.64%, confirming that token generation operates under strict positional constraints rather than free phonotactic distribution.
  

2. The Heading Anomaly (Herbal A)

When extracting the very first word of each folio entry in Herbal A (110 initial tokens preceding plant illustrations):

• 85.5% (94 out of 110) of these initial tokens fail the standard 4-slot FSM parse.
  
• They behave as structural isolates featuring low-frequency consonants and distinct phonotactic skeletons.
  
• This quantitative asymmetry provides objective evidence for a functional division within the manuscript: an open nominal index (headings) followed by a closed procedural matrix (running text).
  

3. Sequential Markov Transition Constraints

Evaluating the sequence of word classes across sentence and line units demonstrates that token ordering is not a random permutation:

Chi-Square Contingency Test of Class Transitions:

Code:

Chi-square = 335.30,  df = 9,  p-value = 8.29e-67

Transition Matrix (%):

Code:

To            C0_Substance  C1_Quality  C2_Operation  C3_Other From                                                          C0_Substance        11.22      20.70        18.40    49.68 C1_Quality            9.14      14.57        30.96    45.33 C2_Operation          8.24      17.43        30.16    44.17 C3_Other              7.87      15.92        23.69    52.53

4. Word-Level Gemination (W W): Evidence Against Dittography

Immediate word repetitions (qokeedy qokeedy, chol chol, shedy shedy) have frequently been interpreted as mechanical scribal errors (dittographies caused by eye-skips). We quantified exact duplicates and root-level geminations across all thematic sections of the manuscript:

Code:

+--------------+-------------+------------------+-----------------+-------------------+ | Section      | Total Pairs | Exact Dups (W W) | Root Gemination | Combined Index    | +--------------+-------------+------------------+-----------------+-------------------+ | Balneo      |    5,128    |      1.27%      |      4.06%      |      5.32%        | | Recipes      |    8,272    |      0.91%      |      3.95%      |      4.86%        | | Herbal B    |    1,110    |      0.63%      |      3.87%      |      4.50%        | | Herbal A    |    7,335    |      1.05%      |      3.22%      |      4.27%        | | Astro/Zodiac |    1,933    |      0.57%      |      3.67%      |      4.24%        | | Pharma      |    2,834    |      0.85%      |      2.96%      |      3.81%        | | Cosmo        |    1,428    |      0.49%      |      2.94%      |      3.43%        | +--------------+-------------+------------------+-----------------+-------------------+

Key Observation:
Gemination density peaks sharply in technical and procedural sections (Balneo at 5.32%, Recipes at 4.86%), while dropping significantly in astronomical diagrams (0.57%) and cosmological schemes (0.49%). Because scribal fatigue should correlate with text volume or line density rather than thematic illustration style, this distribution indicates that gemination functions as a deliberate operational iteration modifier (coque et recoque).

5. Sectional Specialization & Negative Control

Operational Predicates (qo-):
The frequency of action-initiating prefixes (qo-) drops to 2.01% in Astro/Zodiac, compared to 16.53% in Recipes and 23.28% in Balneo. This demonstrates that circular astronomical texts operate as catalogical registries, while Balneo and Recipes serve an operational function.

Phase Co-occurrence (ol vs. ee):
The co-occurrence of liquid phase markers (ol and ee) within individual lines is statistically significant:

Code:

Odds Ratio = 2.303,  Chi-square = 156.96,  p-value = 5.21e-36

Negative Control: Testing Macro-Humoral Polarity:
To test whether whole-page macro-profiles correlate with classical Galenic plant classifications (Circa Instans), we performed a Monte Carlo permutation test (N = 10,000 iterations) matching che- (warm) vs. cho- (cold) against medieval reference catalogs:

• Observed Agreement: 52.00%
  
• Null-Hypothesis Mean: 39.13% (+/- 7.67%)
  
• Effect Size: z = +1.677
  
• Empirical p-value: p = 0.1156
  

Conclusion: The null hypothesis cannot be rejected at the macro-level (p = 0.1156 > 0.05). Whole-page Voynichese text profiles cannot be reliably mapped to binary Galenic plant properties without collapsing into statistical noise. This demonstrates the danger of relying on short 2–3 consonant skeletal matches.

6. Summary and Discussion

The empirical data indicates that MS 408 is structured as an artificial, positional state-machine-driven procedural formulary with clear functional divergence between sections, rather than natural spoken syntax encrypted via substitution cipher.
The complete Python script used to parse the corpus and produce these statistics is attached.

P.S. Research Methodology & AI Assistance Disclosure:

For full transparency regarding the research workflow:

1. The Chain of Hypotheses: Our investigation originated from the hypothesis that Voynichese behaves not as a natural spoken tongue, but as a modular, artificial recording system (a procedural laboratory or apothecary formulary). We formalized this into a 4-slot deterministic finite state machine (FSM). We subsequently tested whether running text reflects algorithmic recipes (evaluating sequential Markov constraints and procedural word gemination W W), and whether page headings function as an open nominal registry. Finally, we instituted a negative control to test whether folio-level macro-profiles could map directly to classical Galenic humoral classifications (Circa Instans), which our permutation test properly refuted (p = 0.1156).
   
2. Use of AI / LLM Tools: An AI assistant (Large Language Model) was utilized as an interactive computational co-pilot throughout this project. It was employed to rapidly generate, refactor, and debug the Python data-processing pipelines in Google Colab, compute statistical tests (chi-square contingency, information-theoretic entropy, Monte Carlo permutations), and structure the mathematical formulation of our findings into this presentation. All data, counts, and statistical outputs presented here were generated deterministically by the attached Python script running on the raw ZL transcription.