HALOWERKDatenvertragswerk
binary necklace orbit inventory audit
For a supplied length1..10 generate ALL binary necklaces under cyclic rotation, represented by lexicographically least0/1word, in increasing lexical order. Return each full word, its least positive cyclic period and orbit size; total necklaces, primitive necklaces with period=n and ascending divisor-period class histogram including zero bins. Sum of orbit sizes covers all2^n binary words. No reflection quotient, color relabeling or density restriction. This is full class-inventory synthesis,.
POST https://datenvertrag.halowerk.com/v1/binary-necklace-orbit-inventory-auditEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| length | Siehe Schema | Ja | |
| claimed_value | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"properties": {
"length": {
"anyOf": [
{
"type": "integer",
"minimum": 1,
"maximum": 10
},
{
"type": "null"
}
]
},
"claimed_value": {
"anyOf": [
{
"type": "object",
"properties": {
"length": {
"type": "integer",
"minimum": 1,
"maximum": 10
},
"necklace_count": {
"type": "integer",
"minimum": 0,
"maximum": 1024
},
"primitive_count": {
"type": "integer",
"minimum": 0,
"maximum": 1024
},
"representatives": {
"type": "array",
"maxItems": 108,
"items": {
"type": "object",
"properties": {
"word": {
"type": "string",
"pattern": "^[01]{1,10}$"
},
"period": {
"type": "integer",
"minimum": 1,
"maximum": 10
},
"orbit_size": {
"type": "integer",
"minimum": 1,
"maximum": 10
}
},
"required": [
"word",
"period",
"orbit_size"
],
"additionalProperties": false
}
},
"period_counts": {
"type": "array",
"maxItems": 10,
"items": {
"type": "object",
"properties": {
"period": {
"type": "integer",
"minimum": 1,
"maximum": 10
},
"classes": {
"type": "integer",
"minimum": 0,
"maximum": 1024
}
},
"required": [
"period",
"classes"
],
"additionalProperties": false
}
}
},
"required": [
"length",
"necklace_count",
"primitive_count",
"representatives",
"period_counts"
],
"additionalProperties": false
},
{
"type": "null"
}
]
}
},
"required": [
"length",
"claimed_value"
],
"additionalProperties": false
}Veröffentlichtes Eingabebeispiel
{
"length": 4,
"claimed_value": {
"length": 4,
"necklace_count": 6,
"primitive_count": 3,
"representatives": [
{
"word": "0000",
"period": 1,
"orbit_size": 1
},
{
"word": "0001",
"period": 4,
"orbit_size": 4
},
{
"word": "0011",
"period": 4,
"orbit_size": 4
},
{
"word": "0101",
"period": 2,
"orbit_size": 2
},
{
"word": "0111",
"period": 4,
"orbit_size": 4
},
{
"word": "1111",
"period": 1,
"orbit_size": 1
}
],
"period_counts": [
{
"period": 1,
"classes": 2
},
{
"period": 2,
"classes": 1
},
{
"period": 4,
"classes": 3
}
]
}
}Ergebnis & Dokumentation
Maschinenlesbare Dokumentation dieses Hubs
Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
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