Pith Number

pith:G2ZIP3OW

pith:2017:G2ZIP3OWPZQMJQZRGBYLFOOEJE

not attested not anchored not stored refs pending

On Optimal 2- and 3-Planar Graphs

Chrysanthi N. Raftopoulou, Michael A. Bekos, Michael Kaufmann

arxiv:1703.06526 v1 · 2017-03-19 · 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{G2ZIP3OWPZQMJQZRGBYLFOOEJE}

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	2026-05-18T00:48:22.590348Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36b287edd67e60c4c3313070b2b9c4490e1dbda9cc5cb625177af6734cc08caf

Aliases

arxiv: 1703.06526 · arxiv_version: 1703.06526v1 · doi: 10.48550/arxiv.1703.06526 · pith_short_12: G2ZIP3OWPZQM · pith_short_16: G2ZIP3OWPZQMJQZR · pith_short_8: G2ZIP3OW

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/G2ZIP3OWPZQMJQZRGBYLFOOEJE \
  | 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: 36b287edd67e60c4c3313070b2b9c4490e1dbda9cc5cb625177af6734cc08caf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59bd68494268d06eb2bde8316becdb46e44d001d6b90f1f7c4e99d482056697c",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2017-03-19T22:13:17Z",
    "title_canon_sha256": "787a47cce5c944321f5a5374880e5a48c76fe9dc69b4c7ae65e1e18893d18888"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.06526",
    "kind": "arxiv",
    "version": 1
  }
}