Pith Number

pith:VV4VGQZW

pith:2011:VV4VGQZWLJ2NPEGXJUWEKKM2ET

not attested not anchored not stored refs pending

On perfect packings in dense graphs

Alexandr V. Kostochka, Andrew Treglown, J\'ozsef Balogh

arxiv:1110.3490 v2 · 2011-10-16 · 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{VV4VGQZWLJ2NPEGXJUWEKKM2ET}

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	2026-05-18T03:31:32.921727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad795343365a74d790d74d2c45299a24cb395fe2dd684b17d672ad41498fa1ca

Aliases

arxiv: 1110.3490 · arxiv_version: 1110.3490v2 · doi: 10.48550/arxiv.1110.3490 · pith_short_12: VV4VGQZWLJ2N · pith_short_16: VV4VGQZWLJ2NPEGX · pith_short_8: VV4VGQZW

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/VV4VGQZWLJ2NPEGXJUWEKKM2ET \
  | 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: ad795343365a74d790d74d2c45299a24cb395fe2dd684b17d672ad41498fa1ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80bfc78b38cd9eecf09ba6e49f7d1a8392cf35c7d4da500ca6d6314cb69252b0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-10-16T14:50:44Z",
    "title_canon_sha256": "e8ee879981ff4f1220cfd8acb50dd9ee85610c267599a795dcf451a8977d3381"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3490",
    "kind": "arxiv",
    "version": 2
  }
}