HALOWERKDatenvertragswerk
graph pebbling universal threshold ledger
For a fully captured connected simple undirected graph on1..4labels0..n-1, derive for EVERYroot r the minimum q such that EVERY distribution of q nonnegative integer pebbles can send at least one pebble to r. Legal move removes2 from a vertex with at least2 and adds1 at a neighbor, losing1. Output root_numbers in vertexorder, lexicographically first unsolvable distribution of totalq-1 for each root, graph_number=max rootnumbers, and certified pigeonhole upperbounds.
POST https://datenvertrag.halowerk.com/v1/graph-pebbling-universal-threshold-ledgerEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| graph | Siehe Schema | Ja | |
| claimed_thresholds | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"additionalProperties": false,
"required": [
"graph",
"claimed_thresholds"
],
"properties": {
"graph": {
"anyOf": [
{
"type": "object",
"additionalProperties": false,
"required": [
"n",
"edges"
],
"properties": {
"n": {
"type": "integer",
"minimum": 1,
"maximum": 4
},
"edges": {
"type": "array",
"maxItems": 6,
"items": {
"type": "array",
"maxItems": 2,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 2
}
}
}
},
{
"type": "null"
}
]
},
"claimed_thresholds": {
"anyOf": [
{
"type": "object",
"additionalProperties": false,
"required": [
"root_numbers",
"bad_distributions",
"graph_number",
"upper_bounds"
],
"properties": {
"root_numbers": {
"type": "array",
"maxItems": 4,
"items": {
"type": "integer",
"minimum": 1,
"maximum": 12
}
},
"bad_distributions": {
"type": "array",
"maxItems": 4,
"items": {
"type": "array",
"maxItems": 4,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 11
}
}
},
"graph_number": {
"type": "integer",
"minimum": 1,
"maximum": 12
},
"upper_bounds": {
"type": "array",
"maxItems": 4,
"items": {
"type": "integer",
"minimum": 1,
"maximum": 12
}
}
}
},
{
"type": "null"
}
]
}
}
}Veröffentlichtes Eingabebeispiel
{
"graph": {
"n": 4,
"edges": [
[
0,
1
],
[
1,
2
],
[
2,
3
]
]
},
"claimed_thresholds": {
"root_numbers": [
8,
5,
5,
8
],
"bad_distributions": [
[
0,
0,
0,
7
],
[
1,
0,
0,
3
],
[
3,
0,
0,
1
],
[
7,
0,
0,
0
]
],
"graph_number": 8,
"upper_bounds": [
12,
6,
6,
12
]
}
}Ergebnis & Dokumentation
Maschinenlesbare Dokumentation dieses Hubs
Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
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