Pith Number

pith:H4LGJJ6V

pith:2017:H4LGJJ6VLOMP2Y2I7RWBGHHVRP

not attested not anchored not stored refs pending

Beyond-Planarity: Density Results for Bipartite Graphs

Maximilian Pfister, Michael A. Bekos, Michael Kaufmann, Patrizio Angelini, Torsten Ueckerdt

arxiv:1712.09855 v1 · 2017-12-28 · cs.DM · cs.CG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H4LGJJ6VLOMP2Y2I7RWBGHHVRP}

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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.

Cited by

1 paper in Pith

Some remarks on the midrange crossing constant

Receipt and verification

First computed	2026-05-18T00:27:05.374160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f1664a7d55b98fd6348fc6c131cf58bcd772849de642c44e82082ad05dfdb29

Aliases

arxiv: 1712.09855 · arxiv_version: 1712.09855v1 · doi: 10.48550/arxiv.1712.09855 · pith_short_12: H4LGJJ6VLOMP · pith_short_16: H4LGJJ6VLOMP2Y2I · pith_short_8: H4LGJJ6V

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/H4LGJJ6VLOMP2Y2I7RWBGHHVRP \
  | 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: 3f1664a7d55b98fd6348fc6c131cf58bcd772849de642c44e82082ad05dfdb29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1eb2ebe56501616293a0edbb2a2b1835126b82392b71c2d49d78521cd434265",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2017-12-28T13:34:37Z",
    "title_canon_sha256": "2ed6bfad770acd708efb9f03d2f80fc6774b48993541511c31ed045ce958819a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.09855",
    "kind": "arxiv",
    "version": 1
  }
}