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christoffel boundary path ledger

For coprime east/north counts from1to8 with total at most12, reconstruct the lower and upper Christoffel words of slope north/east. Symbol0 moves east,1 moves north. Return both whole words and all vertices including endpoints, each with signed line_cross=east*y-north*x. Lower stays at/below the diagonal and is the lexicographically greatest such monotone word; upper is the least word at/above it. No actual coordinates, units, drawing accuracy or wave-stiffness tensor. Compare the whole.

POST https://datenvertrag.halowerk.com/v1/christoffel-boundary-path-ledger

Eingaben

Felder des veröffentlichten Eingabeschemas
FeldTypPflichtBeschreibung
eastSiehe SchemaJa
northSiehe SchemaJa
claimed_wordsSiehe SchemaJa
Vollständiges Eingabeschema anzeigen
{
  "$schema": "http://json-schema.org/draft-07/schema#",
  "type": "object",
  "additionalProperties": false,
  "required": [
    "east",
    "north",
    "claimed_words"
  ],
  "properties": {
    "east": {
      "anyOf": [
        {
          "type": "integer",
          "minimum": 1,
          "maximum": 8
        },
        {
          "type": "null"
        }
      ]
    },
    "north": {
      "anyOf": [
        {
          "type": "integer",
          "minimum": 1,
          "maximum": 8
        },
        {
          "type": "null"
        }
      ]
    },
    "claimed_words": {
      "anyOf": [
        {
          "type": "object",
          "additionalProperties": false,
          "required": [
            "lower",
            "upper"
          ],
          "properties": {
            "lower": {
              "type": "array",
              "maxItems": 12,
              "items": {
                "type": "integer",
                "minimum": 0,
                "maximum": 1
              }
            },
            "upper": {
              "type": "array",
              "maxItems": 12,
              "items": {
                "type": "integer",
                "minimum": 0,
                "maximum": 1
              }
            }
          }
        },
        {
          "type": "null"
        }
      ]
    }
  }
}

Originalschema öffnen

Veröffentlichtes Eingabebeispiel

{
  "east": 7,
  "north": 4,
  "claimed_words": {
    "lower": [
      0,
      0,
      1,
      0,
      0,
      1,
      0,
      0,
      1,
      0,
      1
    ],
    "upper": [
      1,
      0,
      1,
      0,
      0,
      1,
      0,
      0,
      1,
      0,
      0
    ]
  }
}

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Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.

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