Pith Number

pith:2OBA7CFY

pith:2008:2OBA7CFY455R7UC4J5GKQBRI6F

not attested not anchored not stored refs pending

On the Kuratowski graph planarity criterion

A. Skopenkov

arxiv:0802.3820 v3 · 2008-02-26 · math.GT · 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{2OBA7CFY455R7UC4J5GKQBRI6F}

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	2026-05-18T02:32:46.716194Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3820f88b8e77b1fd05c4f4ca80628f15fc5591168989d9c01d6d4edccea0fc3

Aliases

arxiv: 0802.3820 · arxiv_version: 0802.3820v3 · doi: 10.48550/arxiv.0802.3820 · pith_short_12: 2OBA7CFY455R · pith_short_16: 2OBA7CFY455R7UC4 · pith_short_8: 2OBA7CFY

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/2OBA7CFY455R7UC4J5GKQBRI6F \
  | 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: d3820f88b8e77b1fd05c4f4ca80628f15fc5591168989d9c01d6d4edccea0fc3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63b89d16f5888cd1ec4a7824cebc86cda02393e3fecb0a5ea0b09447e98b37f8",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-02-26T15:17:51Z",
    "title_canon_sha256": "48488f09a259dcbf52b6a0c231aea9b7262bc21903e2fe171427d22d6382c042"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0802.3820",
    "kind": "arxiv",
    "version": 3
  }
}