Pith Number

pith:GBN7AEEA

pith:2016:GBN7AEEAKM4W7GFQCAOXRU5HUG

not attested not anchored not stored refs pending

Dynamic Monopolies for Degree Proportional Thresholds in Connected Graphs of Girth at least Five and Trees

Dieter Rautenbach, Michael Gentner

arxiv:1601.02099 v2 · 2016-01-09 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GBN7AEEAKM4W7GFQCAOXRU5HUG}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:20:50.065815Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

305bf0108053396f98b0101d78d3a7a19e69a4840cdead6ca86a7cd8079f6e13

Aliases

arxiv: 1601.02099 · arxiv_version: 1601.02099v2 · doi: 10.48550/arxiv.1601.02099 · pith_short_12: GBN7AEEAKM4W · pith_short_16: GBN7AEEAKM4W7GFQ · pith_short_8: GBN7AEEA

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GBN7AEEAKM4W7GFQCAOXRU5HUG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 305bf0108053396f98b0101d78d3a7a19e69a4840cdead6ca86a7cd8079f6e13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "633f00822a788cf01540c1c38130ac690d36d98b5ac09ab1ae4b345a6141b4a7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-01-09T12:06:15Z",
    "title_canon_sha256": "d0f662be83e1d6853d5b9b9b267b2df54c68ce02ffeec1ef760f674424d66cb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.02099",
    "kind": "arxiv",
    "version": 2
  }
}