Pith Number

pith:FGD4KN6I

pith:2013:FGD4KN6I37A37K2F36CVVOUV6W

not attested not anchored not stored refs pending

Size of edge-critical uniquely 3-colorable planar graphs

Enqiang Zhu, Jin Xu, Zehui Shao, Zepeng Li

arxiv:1312.7495 v1 · 2013-12-29 · 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{FGD4KN6I37A37K2F36CVVOUV6W}

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	2026-05-18T03:03:43.307592Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2987c537c8dfc1bfab45df855aba95f5a1ee6dd65e51d778d83391f48d6e4a69

Aliases

arxiv: 1312.7495 · arxiv_version: 1312.7495v1 · doi: 10.48550/arxiv.1312.7495 · pith_short_12: FGD4KN6I37A3 · pith_short_16: FGD4KN6I37A37K2F · pith_short_8: FGD4KN6I

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/FGD4KN6I37A37K2F36CVVOUV6W \
  | 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: 2987c537c8dfc1bfab45df855aba95f5a1ee6dd65e51d778d83391f48d6e4a69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1145e7cfde7c24898eae265655b72c4b54062b4d1523b282a102fe96572fae38",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-12-29T03:40:26Z",
    "title_canon_sha256": "0b6cb2f3fe46d90bd929e6de1303fff0b16d625cfc9e151f1287cf278b390875"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7495",
    "kind": "arxiv",
    "version": 1
  }
}