Pith Number

pith:P327W445

pith:2011:P327W445U7WKYKNZAHKEXAD6GY

not attested not anchored not stored refs pending

On the bend-number of planar and outerplanar graphs

Daniel Heldt, Kolja Knauer, Torsten Ueckerdt

arxiv:1112.3353 v1 · 2011-12-14 · math.CO · 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{P327W445U7WKYKNZAHKEXAD6GY}

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	2026-05-18T04:06:18.769758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ef5fb739da7ecac29b901d44b807e363fa68f4e315febcc0b056d154c2f92b1

Aliases

arxiv: 1112.3353 · arxiv_version: 1112.3353v1 · doi: 10.48550/arxiv.1112.3353 · pith_short_12: P327W445U7WK · pith_short_16: P327W445U7WKYKNZ · pith_short_8: P327W445

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/P327W445U7WKYKNZAHKEXAD6GY \
  | 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: 7ef5fb739da7ecac29b901d44b807e363fa68f4e315febcc0b056d154c2f92b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7227ab0c23c7d8a02c0a69215eedbe6d5d6d39dfbde0efaa2c700e02a1c7c374",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-14T21:01:24Z",
    "title_canon_sha256": "7ba00d1f11769fbc6459b94cff8b9720d82a0ae24731a509cfdde4ff3b71e36a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3353",
    "kind": "arxiv",
    "version": 1
  }
}