Pith Number

pith:CKUBQ7WJ

pith:2013:CKUBQ7WJUHJPDFPIDKFDC55H7N

not attested not anchored not stored refs pending

The generalized 3-connectivity of random graphs

Ran Gu, Xueliang Li, Yongtang Shi

arxiv:1303.5171 v1 · 2013-03-21 · 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{CKUBQ7WJUHJPDFPIDKFDC55H7N}

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	2026-05-18T03:30:14.292303Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12a8187ec9a1d2f195e81a8a3177a7fb5277b6ae447e9572aceda9a74880ad3d

Aliases

arxiv: 1303.5171 · arxiv_version: 1303.5171v1 · doi: 10.48550/arxiv.1303.5171 · pith_short_12: CKUBQ7WJUHJP · pith_short_16: CKUBQ7WJUHJPDFPI · pith_short_8: CKUBQ7WJ

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/CKUBQ7WJUHJPDFPIDKFDC55H7N \
  | 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: 12a8187ec9a1d2f195e81a8a3177a7fb5277b6ae447e9572aceda9a74880ad3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5042bebaf5f66b25109897948585f658dab3ed6c76c9590a0790eea6eef25df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-03-21T05:40:07Z",
    "title_canon_sha256": "35fd3a0cd18822bb2c448678882ac2b035834cf6a4ad66936ab42c5005f41125"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.5171",
    "kind": "arxiv",
    "version": 1
  }
}