@ Mauro Is this an answer to my post You are not allowed to view links. Register or Login to view.? yes, it was 
Thanks for the clarification.
Since I still can't write Python myself and am not an expert in entropy calculations, I asked Claude and ChatGPT independently of each other. Getting both to produce nearly identical values was more complicated than I thought, but I hope it is correct now...
The following had to be clarified beforehand:
In order to achieve comparable results, I had to normalise the German texts to the standard letters (26 alphabet). The recipe text (Kochrezept) contains only 24 letters, as j (written as i) and q (only in Latin loanwords) do not occur in this small corpus.
I normalised VMS to the standard glyphs: a, ch, cfh, ckh, cph, cth, d, e, f, i, k, l, m, n, o, p, q, r, s, sh, t, y, in order to be able to compare them.
I myself use a cleaned-up EVA file, in which some labels are also missing, provided they are single letters. All special characters in EVA were also removed for the calculation.
Legend:
H1 — Unigram character entropy (bit)
H1 norm — H1 / log₂(alphabet), normalised to alphabet size
H(X₁,X₂) — Joint bigram entropy (bit)
H(X₂|X₁) — Conditional character entropy = H(X₁,X₂) − H1 (Shannon 2nd order)
Vocab — Number of different word types
Hw — Word entropy (bit)
Key findings:
H1 norm: VMS (0.865) lies in the middle of the MHD texts (0.871–0.901) → no anomaly signal at character level
H(X₂|X₁): VMS (2.503) significantly lower than MHD (3.22–3.50) → high predictability of character strings, explainable by fixed prefix patterns of the absorption cipher
Hw: VMS (10.267) higher than all MHD texts → the cipher generates many word types with relatively few tokens through prefix combinations
The combination of low H(X₂|X₁) and high Hw corresponds exactly to the entropy profile that absorption encryption could generate – the highly predictable character strings result from fixed prefixes, but it increased the diversity at the word level through combinatorial prefix attachment. This profile is not to be expected when generating meaningless text, during self-copying processes, or in unencrypted natural language.
An additional factor to consider: all MHD comparison texts are written in normalised literary language, not in phonetic dialect. Phonetically written Bavarian would have lower entropy than standard MHD due to consonants neutralisation (p/b, t/d, k/g merging), vowel reduction (a→o), and syllable-final reduction (-en→-n or dropped entirely). This would close the remaining H1 gap (0.25 bit) further.
The Admonter Bartholomäus comes closest, but is still partially normalised.
Thanks for the clarification.Since I still can't write Python myself and am not an expert in entropy calculations, I asked Claude and ChatGPT independently of each other. Getting both to produce nearly identical values was more complicated than I thought, but I hope it is correct now...
The following had to be clarified beforehand:
In order to achieve comparable results, I had to normalise the German texts to the standard letters (26 alphabet). The recipe text (Kochrezept) contains only 24 letters, as j (written as i) and q (only in Latin loanwords) do not occur in this small corpus.
I normalised VMS to the standard glyphs: a, ch, cfh, ckh, cph, cth, d, e, f, i, k, l, m, n, o, p, q, r, s, sh, t, y, in order to be able to compare them.
I myself use a cleaned-up EVA file, in which some labels are also missing, provided they are single letters. All special characters in EVA were also removed for the calculation.
Legend:
H1 — Unigram character entropy (bit)
H1 norm — H1 / log₂(alphabet), normalised to alphabet size
H(X₁,X₂) — Joint bigram entropy (bit)
H(X₂|X₁) — Conditional character entropy = H(X₁,X₂) − H1 (Shannon 2nd order)
Vocab — Number of different word types
Hw — Word entropy (bit)
Key findings:
H1 norm: VMS (0.865) lies in the middle of the MHD texts (0.871–0.901) → no anomaly signal at character level
H(X₂|X₁): VMS (2.503) significantly lower than MHD (3.22–3.50) → high predictability of character strings, explainable by fixed prefix patterns of the absorption cipher
Hw: VMS (10.267) higher than all MHD texts → the cipher generates many word types with relatively few tokens through prefix combinations
The combination of low H(X₂|X₁) and high Hw corresponds exactly to the entropy profile that absorption encryption could generate – the highly predictable character strings result from fixed prefixes, but it increased the diversity at the word level through combinatorial prefix attachment. This profile is not to be expected when generating meaningless text, during self-copying processes, or in unencrypted natural language.
An additional factor to consider: all MHD comparison texts are written in normalised literary language, not in phonetic dialect. Phonetically written Bavarian would have lower entropy than standard MHD due to consonants neutralisation (p/b, t/d, k/g merging), vowel reduction (a→o), and syllable-final reduction (-en→-n or dropped entirely). This would close the remaining H1 gap (0.25 bit) further.
The Admonter Bartholomäus comes closest, but is still partially normalised.