Pith Number

pith:CG4XB7WR

pith:2011:CG4XB7WRQOOIKO5PDRO7FEWSZZ

not attested not anchored not stored refs pending

An improved upper bound for the bondage number of graphs on surfaces

Jia Huang

arxiv:1111.5629 v3 · 2011-11-23 · 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{CG4XB7WRQOOIKO5PDRO7FEWSZZ}

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	2026-05-18T03:42:23.984811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11b970fed1839c853baf1c5df292d2ce715b230c1d975a9fbe6306e63fc1e12d

Aliases

arxiv: 1111.5629 · arxiv_version: 1111.5629v3 · doi: 10.48550/arxiv.1111.5629 · pith_short_12: CG4XB7WRQOOI · pith_short_16: CG4XB7WRQOOIKO5P · pith_short_8: CG4XB7WR

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/CG4XB7WRQOOIKO5PDRO7FEWSZZ \
  | 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: 11b970fed1839c853baf1c5df292d2ce715b230c1d975a9fbe6306e63fc1e12d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c93422fbed30df2c628b4c0906c5162b8299fbfe74f8cf1b6900cf0383b6a72",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-11-23T21:21:56Z",
    "title_canon_sha256": "203fb0f0ab4f90325d2d9ac78b6c152527ca60d7adf949192122bc17445346ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5629",
    "kind": "arxiv",
    "version": 3
  }
}