{
  "updated": "2026-11-05",
  "author": {
    "name": "Anibal Edelberto Amiot",
    "orcid": "0009-0002-6414-9448",
    "wikidata": "Q141191562",
    "url": "https://anibal-amiot.com"
  },
  "ai_use": {
    "en": "Verification programs, figure scripts and English editing were prepared with AI assistants (Claude, Anthropic; ChatGPT, OpenAI). Each deposit states this use; the author reviews all outputs and is responsible for the content.",
    "fr": "Les programmes de vérification, les scripts des figures et la relecture de l'anglais ont été préparés avec des assistants d'IA (Claude, Anthropic ; ChatGPT, OpenAI). Chaque dépôt le déclare ; l'auteur relit tout et répond du contenu."
  },
  "groups": {
    "Book": {"en": "Book", "fr": "Livre"},
    "Ansate cross and even-order magic squares": {"en": "Ansate cross and even-order magic squares", "fr": "Croix ansée et carrés magiques d'ordre pair"},
    "Patterns, axes and level sets": {"en": "Patterns, axes and level sets", "fr": "Motifs, axes et lignes de niveau"},
    "Doubling modulo n": {"en": "Doubling modulo n", "fr": "Doublement modulo n"},
    "Reports": {"en": "Reports", "fr": "Comptes rendus"}
  },
  "conventions": [
    {"en": "Four numerical readings of a grid of order n, with C = n² + 1: B (blue) = nr + c + 1, R (red) = C − B, V (grey) = nr + n − c, J (yellow) = C − V.", "fr": "Quatre lectures numériques d'une grille d'ordre n, avec C = n² + 1 : B (bleu) = nr + c + 1, R (rouge) = C − B, V (gris) = nr + n − c, J (jaune) = C − V."},
    {"en": "The two order-six ansate crosses are numbered cross 1 and cross 2 in the papers; cross 2 is the cross of the book's reference square. The plates of the book name them EGO and ALTER.", "fr": "Les articles numérotent les deux croix ansées d'ordre six croix 1 et croix 2 ; la croix 2 est celle du carré de référence du livre. Les planches du livre les nomment EGO et ALTER."},
    {"en": "Alpha and omega are the cells of the smallest and largest numbers of a square (1 and 36 at order six).", "fr": "Alpha et oméga désignent les cases du plus petit et du plus grand nombre d'un carré (1 et 36 à l'ordre six)."},
    {"en": "Merging blue and red gives the three-tint (tricolour) patterns; the four-colour, three-colour and two-colour systems descend from one another.", "fr": "La fusion du bleu et du rouge donne les motifs à trois teintes (tricolores) ; les systèmes quadricolore, tricolore et bicolore descendent l'un de l'autre."}
  ],
  "works": [
    {
      "id": "livree-hermes", "group": "Book", "type": "book",
      "title": "La Livrée d'Hermès",
      "summary_en": "Arithmogeometry of magic squares and their transcription into a Jacquard pattern system; eight language editions.",
      "summary_fr": "Arithmogéométrie des carrés magiques et leur transcription en un système de motifs pour métier Jacquard ; huit éditions linguistiques.",
      "version": "3.0", "date": "2026-10-06",
      "status_en": "Published (open access)", "status_fr": "Publié (accès libre)",
      "doi": "10.5281/zenodo.22722485", "version_doi": "10.5281/zenodo.23184828", "license": "CC BY-NC 4.0", "pending": false
    },
    {
      "id": "plaques-360", "group": "Book", "type": "dataset",
      "title": "Chapitre VIII — Le Jeu : Les 360 plaques ajourées de La Livrée d'Hermès",
      "summary_en": "STL, 3MF and SVG models of the 360 perforated plates, with generation scripts and bilingual documentation.",
      "summary_fr": "Modèles STL, 3MF et SVG des 360 plaques ajourées, avec les scripts de génération et une documentation bilingue.",
      "version": "3.1", "date": "2026-10-06",
      "status_en": "Published", "status_fr": "Publié",
      "doi": "10.5281/zenodo.23189275", "version_doi": "10.5281/zenodo.23189276", "license": "CC BY-NC 4.0", "pending": false
    },
    {
      "id": "ansate-cross-order6", "group": "Ansate cross and even-order magic squares", "type": "article",
      "title": "The Ansate Cross: A Self-Constructing Method for Order-6 Magic Squares",
      "summary_en": "The two order-six ansate crosses and the 256 colourings of the book that give magic squares. Under review; the manuscript is not public during review. Its code and data are in the verification-code record.",
      "summary_fr": "Les deux croix ansées d'ordre six et les 256 colorations du livre qui donnent des carrés magiques. En évaluation ; le manuscrit n'est pas public pendant l'évaluation. Son code et ses données sont dans la fiche du code de vérification.",
      "version": "v3.5", "date": "2026-11-05",
      "status_en": "Under review (Mathematics Magazine)", "status_fr": "En évaluation (Mathematics Magazine)",
      "doi": null, "version_doi": null, "pending": false
    },
    {
      "id": "ansate-cross-general", "group": "Ansate cross and even-order magic squares", "type": "preprint",
      "title": "The Ansate Cross: Even-Order Realisation and Singly Even Colour Symmetry",
      "summary_en": "A pointwise four-class protocol for even-order magic squares: a common realisation theorem, the strict case, colour symmetry at singly even orders 6t (t odd), and growth by a periodic antipodal support. English and French, revision 223.",
      "summary_fr": "Un protocole ponctuel à quatre classes pour les carrés magiques d'ordre pair : théorème commun de réalisation, cas strict, symétrie de couleur aux ordres simplement pairs 6t (t impair), croissance par un support antipodal périodique. Anglais et français, révision 223.",
      "version": "223", "date": "2026-11-05",
      "status_en": "Preprint", "status_fr": "Prépublication",
      "doi": "10.5281/zenodo.23269974", "version_doi": "10.5281/zenodo.23978781", "license": "CC BY 4.0 (texts), AGPL-3.0 (code)", "pending": false
    },
    {
      "id": "ansate-cross-code", "group": "Ansate cross and even-order magic squares", "type": "software",
      "title": "The Ansate Cross — verification code and data",
      "summary_en": "Independent audit, verification programs and data for the ansate-cross papers, including the figure scripts of the order-six article.",
      "summary_fr": "Audit indépendant, programmes de vérification et données des articles sur la croix ansée, dont les scripts des figures de l'article d'ordre six.",
      "version": "4.0.1", "date": "2026-11-05",
      "status_en": "Published", "status_fr": "Publié",
      "doi": "10.5281/zenodo.22866061", "version_doi": "10.5281/zenodo.23983584", "license": "AGPL-3.0 (code), CC BY 4.0 (texts), CC BY-NC 4.0 (data)", "pending": false
    },
    {
      "id": "unified-patterns", "group": "Patterns, axes and level sets", "type": "software",
      "title": "Unified Patterns — companion article, data and verification (half-shift criterion on three-colour 12 × 12 grids)",
      "summary_en": "Companion article 'From Ansate Cross Colourings to Unified Patterns and Sound Forms' (v2.20, with supplement C1–C6 and certificates) and the data and scripts of the half-shift note submitted to the Journal of Mathematics and the Arts.",
      "summary_fr": "Article compagnon « Des colorations des croix ansées aux motifs Unified Patterns et aux formes sonores » (v2.20, avec le complément C1–C6 et les certificats), et données et scripts de la note sur le demi-décalage soumise au Journal of Mathematics and the Arts.",
      "version": "2.20", "date": "2026-11-05",
      "status_en": "Half-shift note under review (Journal of Mathematics and the Arts); companion article: preprint", "status_fr": "Note du demi-décalage en évaluation (Journal of Mathematics and the Arts) ; article compagnon : prépublication",
      "doi": "10.5281/zenodo.22862110", "version_doi": "10.5281/zenodo.23991050", "license": "AGPL-3.0 (code), CC BY 4.0 (texts)", "pending": false
    },
    {
      "id": "axes-chladni", "group": "Patterns, axes and level sets", "type": "preprint",
      "title": "Axes and Level Sets of a Jacquard Pattern System — two companion notes",
      "summary_en": "A vocabulary of axes generated by an inverse doubling on the 12 × 12 square, and its identification with the level sets of a square-plate eigenmode.",
      "summary_fr": "Un vocabulaire d'axes engendré par un doublement inverse sur le carré 12 × 12, et son identification avec les lignes de niveau d'un mode propre de plaque carrée.",
      "version": "2.15", "date": "2026-11-05",
      "status_en": "Preprint", "status_fr": "Prépublication",
      "doi": "10.5281/zenodo.22965031", "version_doi": "10.5281/zenodo.23990857", "license": "CC BY 4.0 (texts), AGPL-3.0 (code)", "pending": false
    },
    {
      "id": "one-object", "group": "Patterns, axes and level sets", "type": "preprint",
      "title": "One Object, Three Descriptions: Axes, Images and Grids of a Jacquard Pattern System",
      "summary_en": "The axes, the sixty images and the 512 grids of the pattern system are shown, by exhaustive check, to present one finite structure.",
      "summary_fr": "Les axes, les soixante images et les 512 grilles du système de motifs forment une seule structure finie, vérifiée de façon exhaustive.",
      "version": "1.4.0", "date": "2026-11-05",
      "status_en": "Preprint", "status_fr": "Prépublication",
      "doi": "10.5281/zenodo.22986529", "version_doi": "10.5281/zenodo.23986406", "license": "CC BY 4.0 (texts), AGPL-3.0 (code)", "pending": false
    },
    {
      "id": "moire", "group": "Patterns, axes and level sets", "type": "preprint",
      "title": "Parity Figures as Moiré: What Is Exact and What Is Not",
      "summary_en": "Places the parity construction within the theory of moiré and separates what is exact from what is not.",
      "summary_fr": "Situe la construction par parité dans la théorie du moiré et sépare ce qui est exact de ce qui ne l'est pas.",
      "version": "1.0.1", "date": "2026-09-27",
      "status_en": "Preprint", "status_fr": "Prépublication",
      "doi": "10.5281/zenodo.22967584", "version_doi": "10.5281/zenodo.22986645", "license": "CC BY 4.0 (texts), AGPL-3.0 (code)", "pending": false
    },
    {
      "id": "doubling-I-IV", "group": "Doubling modulo n", "type": "preprint",
      "title": "Sign-Quotiented Doubling Modulo n: Cycle Structure, 2-Adic Synchronization, Lifting, and Forward-Closed Subsets — Four Working Papers",
      "summary_en": "Multiplication by 2 on Z/nZ after identifying x with −x, for every n: cycles, 2-adic lifting and the enumeration of forward-closed subsets.",
      "summary_fr": "La multiplication par 2 sur Z/nZ, en identifiant x et −x, pour tout n : cycles, relèvement 2-adique et dénombrement des sous-ensembles fermés vers l'avant.",
      "version": "1.1.1", "date": "2026-10-02",
      "status_en": "Working papers", "status_fr": "Documents de travail",
      "doi": "10.5281/zenodo.23088601", "version_doi": "10.5281/zenodo.23102045", "license": "CC BY 4.0 (texts), AGPL-3.0 (code)", "pending": false
    },
    {
      "id": "log-concavity", "group": "Doubling modulo n", "type": "preprint",
      "title": "Strict Log-Concavity Across All Scales for Exact-Height Plane Binary Trees",
      "summary_en": "Eventual strict log-concavity of the coefficient columns of exact-height plane binary trees; working preprint, not yet read by a specialist.",
      "summary_fr": "Log-concavité stricte, à terme, des colonnes de coefficients des arbres binaires plans de hauteur exacte ; prépublication de travail, pas encore relue par un spécialiste.",
      "version": "1.0.0", "date": "2026-10-02",
      "status_en": "Working preprint", "status_fr": "Prépublication de travail",
      "doi": "10.5281/zenodo.23102264", "version_doi": "10.5281/zenodo.23102265", "license": "CC BY 4.0 (text), AGPL-3.0 (code)", "pending": false
    },
    {
      "id": "subsets-dataset", "group": "Doubling modulo n", "type": "dataset",
      "title": "Number of subsets of Z/nZ closed under negation and doubling: terms to n = 200 and program",
      "summary_en": "Terms a(1)…a(200) and the program that computes them.",
      "summary_fr": "Les termes a(1)…a(200) et le programme qui les calcule.",
      "version": "1.0", "date": "2026-09-27",
      "status_en": "Published", "status_fr": "Publié",
      "doi": "10.5281/zenodo.22991226", "version_doi": "10.5281/zenodo.22991227", "license": "CC BY 4.0 (data), AGPL-3.0 (code)", "pending": false
    },
    {
      "id": "compte-rendu", "group": "Reports", "type": "report",
      "title": "La Livrée d'Hermès — compte rendu de travaux / progress report",
      "summary_en": "Progress report on the work around the book: papers under review, deposits, results and open questions.",
      "summary_fr": "Compte rendu des travaux autour du livre : articles en évaluation, dépôts, résultats et questions ouvertes.",
      "version": "2026.11.05", "date": "2026-11-05",
      "status_en": "Published", "status_fr": "Publié",
      "doi": "10.5281/zenodo.22945021", "version_doi": "10.5281/zenodo.23986580", "pending": false
    }
  ]
}