Pith Number

pith:XLAMIM73

pith:2012:XLAMIM73EZTETFJ7AT6JHFG4CY

not attested not anchored not stored refs pending

An upper bound for the crossing number of bubble-sort graph Bn

Baigong Zheng, Xirong Xu, Yuansheng Yang

arxiv:1211.4433 v1 · 2012-11-19 · cs.DM · 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{XLAMIM73EZTETFJ7AT6JHFG4CY}

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	2026-05-18T03:40:26.943520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bac0c433fb266649953f04fc9394dc1606e05f83a5d760987355005b87d9ad3f

Aliases

arxiv: 1211.4433 · arxiv_version: 1211.4433v1 · doi: 10.48550/arxiv.1211.4433 · pith_short_12: XLAMIM73EZTE · pith_short_16: XLAMIM73EZTETFJ7 · pith_short_8: XLAMIM73

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/XLAMIM73EZTETFJ7AT6JHFG4CY \
  | 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: bac0c433fb266649953f04fc9394dc1606e05f83a5d760987355005b87d9ad3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f16cc777b7af5b619149408a3119da301e9164d7235390dd6a3294abb258f4a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2012-11-19T14:19:38Z",
    "title_canon_sha256": "2f0cc6526d6f888140ecca7080b677517bb5a385e8e0f6ad0b56812da354f50e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4433",
    "kind": "arxiv",
    "version": 1
  }
}