Pith Number

pith:T4KEEBTN

pith:2016:T4KEEBTN6EY3LZQJ4RHP27DRPM

not attested not anchored not stored refs pending

Book crossing numbers of the complete graph and small local convex crossing numbers

Bernardo M. \'Abrego, Evgeniya Lagoda, Julia Dandurand, Silvia Fern\'andez-Merchant, Yakov Sapozhnikov

arxiv:1607.00131 v3 · 2016-07-01 · 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{T4KEEBTN6EY3LZQJ4RHP27DRPM}

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.

Cited by

1 paper in Pith

On the maximum number of edges of outer k-planar graphs

Receipt and verification

First computed	2026-07-05T08:20:05.129911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f1442066df131b5e609e44efd7c717b0995834cf5fcad31be2390248b5587ab

Aliases

arxiv: 1607.00131 · arxiv_version: 1607.00131v3 · doi: 10.48550/arxiv.1607.00131 · pith_short_12: T4KEEBTN6EY3 · pith_short_16: T4KEEBTN6EY3LZQJ · pith_short_8: T4KEEBTN

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/T4KEEBTN6EY3LZQJ4RHP27DRPM \
  | 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: 9f1442066df131b5e609e44efd7c717b0995834cf5fcad31be2390248b5587ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "632f3f4ccfa745a8aa75e10c0f3d98974b402c35c847226d28b993015083aeb9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-07-01T07:21:40Z",
    "title_canon_sha256": "d25775035a457b40e53ba8edcf1486c7c02d80da8924a4249e653f2584257feb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.00131",
    "kind": "arxiv",
    "version": 3
  }
}