Pith Number

pith:52VRXX4W

pith:2019:52VRXX4WYQCMOS6HL7DISPZU75

not attested not anchored not stored refs pending

Crossing Numbers of Beyond-Planar Graphs

Fabrizio Montecchiani, Markus Chimani, Pavel Valtr, Philipp Kindermann

arxiv:1908.03153 v2 · 2019-08-08 · cs.CG · 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{52VRXX4WYQCMOS6HL7DISPZU75}

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	2026-07-05T00:03:00.362538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eeab1bdf96c404c74bc75fc6893f34ff43fdc66b7b38c6c411536dde63f5bd14

Aliases

arxiv: 1908.03153 · arxiv_version: 1908.03153v2 · doi: 10.48550/arxiv.1908.03153 · pith_short_12: 52VRXX4WYQCM · pith_short_16: 52VRXX4WYQCMOS6H · pith_short_8: 52VRXX4W

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/52VRXX4WYQCMOS6HL7DISPZU75 \
  | 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: eeab1bdf96c404c74bc75fc6893f34ff43fdc66b7b38c6c411536dde63f5bd14

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81c906281a3a236e3d6cee24e09644880c9782a642c8ef153b5f1b2aee13db98",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2019-08-08T16:28:12Z",
    "title_canon_sha256": "04a19b3d7d93c4f199fb9ba369de43fade120aae3678e3454c30b1d47c1f345c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03153",
    "kind": "arxiv",
    "version": 2
  }
}