yetzirah

Prototype. This is an experiment beside Mova, not part of its core yet: it works and is measured, but its interfaces and data may change at any time.

Sefer Yetzirah (ספר יצירה) as automata: the twenty-two letters and what the book builds from them, in two classical recensions and a third reading of ours.

What it holds

• The letters: 3 mothers (אמ"ש), 7 doubles (בג"ד כפר"ת), 12 simple letters; the five places of the mouth (2:3).
• The tables of each letter: what it is crowned with, and what it is set over in the world, the year and the soul. Mothers also have their male and female permutations, and doubles have their opposites.
• The six seals: the permutations of י־ה־ו that seal the six directions, the fifth to the tenth sefirah (1:13).
• The 231 gates: every pair of letters, read forward and back (2:4–2:5).
• The houses: "two stones build two houses, three build six …", that is n!, and for a word, the orderings of its letters.

Three automata

• standard: the standard printed (Mantua-type) recension, Warsaw 1884.
• gra: the Vilna Gaon's recension, Warsaw 1884.
• elamur: ours. Where the two agree, it says what they say. Where they differ, it holds both readings, the standard first and the Gra second, until a basis is chosen (elamur::measure). Measured on either basis, it gives back exactly that recension (tested). Our own entries go in elamur::OURS and nowhere else; it starts empty.

Each classical entry carries the exact words of its source (quote), with chapter and mishnah. verify checks every quote against the texts in docs/sefer-yetzirah/text/, and checks every count of houses against n!. A table cannot drift from the book without a test going red, and a negative control shows that red. Where the standard recension does not tie a value to a letter (the qualities of the doubles other than bet, and the senses of the simple letters), the value is taken by the order of the list and marked by list order.

Run

cargo run --release -p yetzirah -- check        # every table against its text
cargo run --release -p yetzirah -- letter ב     # one letter in all three automata
cargo run --release -p yetzirah -- diff         # where the two recensions differ
cargo run --release -p yetzirah -- seals
cargo run --release -p yetzirah -- gates א
cargo run --release -p yetzirah -- word אדם     # letters, gates between them, houses

Measured (2026-10-17)

• Each recension: 101 letter entries, 6 seals and 6 counts of houses, all found in the text.
• The two recensions differ in 54 places:
  • the planets of all seven doubles;
  • the qualities and their opposites;
  • most body parts;
  • the senses of the simple letters;
  • five of the six seals.
• They agree on:
  • the mothers;
  • the signs and months of the simple letters;
  • the days of the doubles;
  • the seal of height (יה"ו).
• Firmness of readings (elamur::firmness):
  • 52 readings are firm: both recensions say the same, and say it outright.
  • 49 are conjectures: the recensions differ.
  • No reading is left 'by list order'. Wherever the standard recension only lists values in the order of the letters, the Gra says something else. Where the text does not tie a value to a letter, the editors had to arrange it, and they arranged it differently. Where the two disagree, their permutations are often guesses.
• The standard recension's planets follow the Chaldean order. It sets the planets on bet … tav exactly in the old order of the planets, Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon. That is a list laid out by an editor rather than a tradition. The Gra lists the planets in the same order in 4:7, but ties them to the letters otherwise, following the Ari. Both points are tested.
• letter shows the firmness of every slot.
• Two runs give the same output, byte for byte.

Limits

The texts are read only in Hebrew, and English glosses are ours. The twelve diagonal boundaries (5:1 standard, 5:2 Gra) are not yet tied to letters, since neither text ties them except by list order. The same goes for the lovers, haters, life-givers and killers of 6:3 / 6:5. The commentaries in docs/sefer-yetzirah/commentaries/ are not yet read in. The automata know no Hebrew grammar: they work on letters, not words.

Licence: Elamur Cosmic License (Elamur Cosmic License). The texts it reads are in the public domain.

This page in Markdown → https://md.mova.elamur.ai/free/en/docs/yetzirah/