HALOWERKDatenvertragswerk
generated transformation monoid audit
From0..3 supplied ordered total state maps on degree1..3 states, reconstructs every generated transformation including identity, its shortest lengthlexicographic generatorword and the whole multiplicationtable. Table[i][j] applies i THEN j, image q -> t_j[t_i[q]]. Identity is index0. Duplicate generators remain distinct commandletters; arrayorder defines canonicalwitnesses and elementorder. Empty generators yield identitymonoid. Whole ordered image/table claim checked, not just cardinality.
POST https://datenvertrag.halowerk.com/v1/generated-transformation-monoid-auditEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| degree | integer | Ja | |
| generators | array | Ja | |
| claimed | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"properties": {
"degree": {
"type": "integer",
"minimum": 1,
"maximum": 3
},
"generators": {
"type": "array",
"maxItems": 3,
"items": {
"type": "array",
"minItems": 1,
"maxItems": 3,
"items": {
"anyOf": [
{
"type": "integer",
"minimum": 0,
"maximum": 2
},
{
"type": "null"
}
]
}
}
},
"claimed": {
"anyOf": [
{
"type": "object",
"properties": {
"transformations": {
"type": "array",
"maxItems": 27,
"items": {
"type": "array",
"maxItems": 3,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 2
}
}
},
"composition_table": {
"type": "array",
"maxItems": 27,
"items": {
"type": "array",
"maxItems": 27,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 26
}
}
}
},
"required": [
"transformations",
"composition_table"
],
"additionalProperties": false
},
{
"type": "null"
}
]
}
},
"required": [
"degree",
"generators",
"claimed"
],
"additionalProperties": false
}Veröffentlichtes Eingabebeispiel
{
"degree": 2,
"generators": [
[
0,
0
]
],
"claimed": {
"transformations": [
[
0,
1
],
[
0,
0
]
],
"composition_table": [
[
0,
1
],
[
1,
1
]
]
}
}Ergebnis & Dokumentation
Maschinenlesbare Dokumentation dieses Hubs
Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
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