Pith Number

pith:JLECA4G3

pith:2012:JLECA4G35THAKNCWASWPUPPRWP

not attested not anchored not stored refs pending

The crossing numbers of $K_m\times P_n$ and $K_m\times C_n$

Baigong Zheng, Xiaohui Lin, Xirong Xu, Yuansheng Yang

arxiv:1211.4641 v1 · 2012-11-20 · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JLECA4G35THAKNCWASWPUPPRWP}

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	2026-05-18T03:40:26.082325Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ac82070dbecce05345604acfa3df1b3d17f6cba517a8b369afd14f577716673

Aliases

arxiv: 1211.4641 · arxiv_version: 1211.4641v1 · doi: 10.48550/arxiv.1211.4641 · pith_short_12: JLECA4G35THA · pith_short_16: JLECA4G35THAKNCW · pith_short_8: JLECA4G3

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/JLECA4G35THAKNCWASWPUPPRWP \
  | 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: 4ac82070dbecce05345604acfa3df1b3d17f6cba517a8b369afd14f577716673

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57819fe1f99f8263d44155983a0d2465cf811347f21da1dfbab0fec028c90d97",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2012-11-20T01:03:09Z",
    "title_canon_sha256": "5855e1140bbde9c3dea2299625392afd6c594079ed40595962000d1e0ebfd0a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4641",
    "kind": "arxiv",
    "version": 1
  }
}