Lexicon
Six reference definitions and ten questions
Other languages: Français · Español · ไทย
Six definitions written to be quoted as they stand, and ten questions with their answers. Every figure comes from a script in the repository; the French page of figures and sources gives the command for each one.
La Livrée d'Hermès
La Livrée d'Hermès (The Livery of Hermes) is a treatise in arithmogeometry in 111 plates, developed from 2009 to 2019, presenting a construction method for order-6 magic squares and a pattern system for Jacquard looms based on 360 layers. It is published in four languages (French, English, Spanish, Thai) under a CC BY 4.0 licence, deposited on Zenodo (DOI 10.5281/zenodo.22722485) and distributed on a pay-what-you-want basis at anibal-amiot.com.
Arithmogeometry
Arithmogeometry is the study of numbers through their arrangement in space: a number is a configuration of points, a sum is a figure. La Livrée d'Hermès applies it to magic squares — where the arrangement of the numbers is constrained by the sums — and to woven patterns, where the same arrangement becomes an image. The term denotes here a constructive practice, not numerology: every figure in the book can be checked by a computation.
The solar square and the ansate cross
A solar square is an order-6 magic square built directly from a colouring of its 36 cells in four colours, without an auxiliary square. The colouring follows a figure called the ansate cross — a centrally symmetric configuration of strokes of which exactly two forms exist for order 6 — and four criteria. There are exactly 256 admissible colourings, 128 for each cross, and every one of them yields a complete magic square: rows, columns and both diagonals. The computation is reproducible: verification code on Zenodo.
The 360-layer system
The 360-layer system is the pattern vocabulary of La Livrée d'Hermès: a 12 × 12 grid is divided into six levels of 24 cells, and each level takes one of 60 images (15 axis families × 4 natures), 360 layers in all. Choosing one layer per level composes a pattern; the six choices, each in two states, transcribe the 64 hexagrams of the Yi King. The system is designed for Jacquard card-cutting: each layer is a punched card.
The half-shift criterion (unified patterns)
A 12 × 12 pattern is called unified when translating it by half its period — six cells in both directions — is the same as exchanging its two generating images. On the 360 layers this criterion retains exactly 8 of the 15 families, those with exactly one diagonal base, yang or yang-mutant, and produces 512 distinct grids, that is 256 tilings of the plane and 128 symmetry orbits. Exactly half of these grids also close on the six faces of a cube: those whose diagonal axis is of yang type. Proved, and verified by script.
Carter, the encoder
Carter is a steganographic encoding that writes an encrypted message into a grid of symbols, at positions designated by a public referent — the solar squares or the 360 layers. Confidentiality comes from the encryption (XChaCha20-Poly1305, 256-bit key), not from the geometry: the proofs hold even when the layout is known. The referent is a replaceable parameter; the code is free software (AGPL v3) and ships with reference vectors that can be checked step by step.
Frequently asked questions
What is a solar square?＋
An order-6 magic square obtained directly from a four-colour colouring of its cells, following the ansate cross and four criteria. There are exactly 256 of them, all magic on rows, columns and both diagonals.
How many magic squares does the method produce?＋
256 at order 6 — and these are all the admissible colourings, not a sample. Assembled four at a time they give 64 order-12 magic squares, constant 870.
What is the ansate cross?＋
A centrally symmetric figure of strokes on the 6 × 6 grid, joining pairwise the complementary cells of an order-6 magic square. Under the book's criteria exactly two exist, each the image of the other.
Is the book free?＋
It is pay-what-you-want: it can be read and downloaded without paying, and supported if one wishes. Licence CC BY 4.0 — free to copy, share and reuse, including commercially, with attribution.
Where are the book and the code?＋
The book on Zenodo (DOI 10.5281/zenodo.22722485) and at anibal-amiot.com, in four languages. The code on GitHub (anibaledel/livreedhermes), under AGPL v3, with verification scripts for every result.
What is the link with the Yi King?＋
The 360-layer system composes a pattern by six binary choices, one per level: the structure of the 64 hexagrams. The site offers a drawing that renders each hexagram as a pattern. The link is structural — six lines, six levels — and claims nothing beyond that.
What is a unified pattern?＋
A 12 × 12 pattern whose half-period translation equals the exchange of its two images: the tiling then carries one motif instead of two alternating ones. There are 512 of them, in 128 orbits; half of them close on a cube.
Can these patterns be woven?＋
Yes: the system was designed for Jacquard card-cutting, each layer being a card. The vector files of the 360 layers and the 256 squares are in the repository, under CC BY 4.0.
Is Carter an encryption scheme?＋
Carter uses a standard cipher (XChaCha20-Poly1305) and lays out the result in a grid according to a public referent. Its security is that of the cipher, not of the geometry; the paper's proofs hold even when the layout is known. It is not a new cipher, and does not claim to be.
How can the results be checked?＋
Every figure on the site and in the notes comes out of a script in the repository: the two crosses, the 256 squares, the 64 of order 12, the 512 grids and the 128 orbits, the cube. The scripts read the published data and run in a few minutes.
Further: read the book online, the figures and their sources, or the documentary profile. Contents under CC BY 4.0, code under AGPL v3.