Pith Number

pith:FGGDOVNU

pith:2015:FGGDOVNUHZXH7KAXALZGULARUK

not attested not anchored not stored refs pending

Constructing a Family of 4-Critical Planar Graphs with High Edge-Density

Yao Tianxing, Zhou Guofei

arxiv:1509.00760 v1 · 2015-09-02 · 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{FGGDOVNUHZXH7KAXALZGULARUK}

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	2026-05-18T01:34:06.110840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

298c3755b43e6e7fa81702f26a2c11a2bede7375861426d4a8079553acde943f

Aliases

arxiv: 1509.00760 · arxiv_version: 1509.00760v1 · doi: 10.48550/arxiv.1509.00760 · pith_short_12: FGGDOVNUHZXH · pith_short_16: FGGDOVNUHZXH7KAX · pith_short_8: FGGDOVNU

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/FGGDOVNUHZXH7KAXALZGULARUK \
  | 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: 298c3755b43e6e7fa81702f26a2c11a2bede7375861426d4a8079553acde943f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c24024ee895da9d888ed15347ac9ed26b625c390b87d2e5e950b3587cc07ff6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-02T15:54:40Z",
    "title_canon_sha256": "c550c9587fdd45ebc93c61939fd67bd954af9cec694b847c43cac93f2ac7838c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.00760",
    "kind": "arxiv",
    "version": 1
  }
}