Pith Number

pith:UWS4KC6Z

pith:2025:UWS4KC6Z6OGRGGWNGAAFLV3FJF

not attested not anchored not stored refs pending

A first view on the density of 5-planar graphs

Aaron B\"ungener, Jakob Franz, Maximilian Pfister, Michael Kaufmann

arxiv:2505.24364 v2 · 2025-05-30 · 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{UWS4KC6Z6OGRGGWNGAAFLV3FJF}

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	2026-05-20T00:00:20.678571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5a5c50bd9f38d131acd300055d7654964a49cfc229260c3cf098848b73a184b

Aliases

arxiv: 2505.24364 · arxiv_version: 2505.24364v2 · doi: 10.48550/arxiv.2505.24364 · pith_short_12: UWS4KC6Z6OGR · pith_short_16: UWS4KC6Z6OGRGGWN · pith_short_8: UWS4KC6Z

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/UWS4KC6Z6OGRGGWNGAAFLV3FJF \
  | 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: a5a5c50bd9f38d131acd300055d7654964a49cfc229260c3cf098848b73a184b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0320d5c7571371688dd6156fd5a165fb084fad47ad08c36a275e814a2fe55fd5",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2025-05-30T08:55:29Z",
    "title_canon_sha256": "a8d101e0ece29b213898a34116b9f1f8650126bf91d23a9a1bc81b2fe74a4041"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.24364",
    "kind": "arxiv",
    "version": 2
  }
}