Pith Number

pith:SGHA7VTL

pith:2012:SGHA7VTLXIXPSQ62Y7LKZTIPKG

not attested not anchored not stored refs pending

A Kuratowski-Type Theorem for Planarity of Partially Embedded Graphs

Ignaz Rutter, Jan Kratochv\'il, V\'it Jel\'inek

arxiv:1204.2915 v1 · 2012-04-13 · 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{SGHA7VTLXIXPSQ62Y7LKZTIPKG}

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	2026-05-18T03:58:02.539301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

918e0fd66bba2ef943dac7d6accd0f5184cd96804d992bd9e81d66f079de988d

Aliases

arxiv: 1204.2915 · arxiv_version: 1204.2915v1 · doi: 10.48550/arxiv.1204.2915 · pith_short_12: SGHA7VTLXIXP · pith_short_16: SGHA7VTLXIXPSQ62 · pith_short_8: SGHA7VTL

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/SGHA7VTLXIXPSQ62Y7LKZTIPKG \
  | 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: 918e0fd66bba2ef943dac7d6accd0f5184cd96804d992bd9e81d66f079de988d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df6c2090cb753dcce9305153c69de1a649f9a4a87bc49fee9dc0708482528746",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2012-04-13T08:28:11Z",
    "title_canon_sha256": "7c1a000638e3796803ce885b097b66f4ada1ca5ef64800080ddeb1b9b2a6fb92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.2915",
    "kind": "arxiv",
    "version": 1
  }
}