Pith Number

pith:RZLCBRKP

pith:2012:RZLCBRKPCXQ4IWR6MH4GAQY5WX

not attested not anchored not stored refs pending

The crossing numbers of $K_{n,n}-nK_2$, $K_{n}\times P_2$, $K_{n}\times P_3$ and $K_n\times C_4$

Baigong Zheng, Xiaohui Lin, Xirong Xu, Yuansheng Yang

arxiv:1211.4437 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{RZLCBRKPCXQ4IWR6MH4GAQY5WX}

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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	2026-05-18T03:40:26.931641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e5620c54f15e1c45a3e61f860431db5ecbcc38b1be7a7597145875160987b01

Aliases

arxiv: 1211.4437 · arxiv_version: 1211.4437v1 · doi: 10.48550/arxiv.1211.4437 · pith_short_12: RZLCBRKPCXQ4 · pith_short_16: RZLCBRKPCXQ4IWR6 · pith_short_8: RZLCBRKP

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/RZLCBRKPCXQ4IWR6MH4GAQY5WX \
  | 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: 8e5620c54f15e1c45a3e61f860431db5ecbcc38b1be7a7597145875160987b01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df588a4152f627f4a5e44a62b7f8f7fad111b77e984d810dfe2547e819a8e2c2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2012-11-19T14:36:17Z",
    "title_canon_sha256": "d1921453f635f8768c65c0bfda2042aa3b25dfd5412292e1ee4e520f92b8b76d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4437",
    "kind": "arxiv",
    "version": 1
  }
}