Pith Number

pith:Y46ESOXD

pith:2017:Y46ESOXDDN4TNK6IRX6F7T5WWD

not attested not anchored not stored refs pending

The k-planar crossing number of random graphs and random regular graphs

Arran Hamm, John Asplund, Laszlo Szekely, Libby Taylor, Thao Do, Zhiyu Wang

arxiv:1709.08136 v1 · 2017-09-24 · 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{Y46ESOXDDN4TNK6IRX6F7T5WWD}

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	2026-05-18T00:34:27.869332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c73c493ae31b7936abc88dfc5fcfb6b0dcd3733ef9d4a1e014d3a7874d493d30

Aliases

arxiv: 1709.08136 · arxiv_version: 1709.08136v1 · doi: 10.48550/arxiv.1709.08136 · pith_short_12: Y46ESOXDDN4T · pith_short_16: Y46ESOXDDN4TNK6I · pith_short_8: Y46ESOXD

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/Y46ESOXDDN4TNK6IRX6F7T5WWD \
  | 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: c73c493ae31b7936abc88dfc5fcfb6b0dcd3733ef9d4a1e014d3a7874d493d30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8eee2ef853934eb8249c092c5eb34a1dfd6e13db35957ac64f0b641814c1115",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-09-24T01:45:10Z",
    "title_canon_sha256": "b2dff9f7894923193f5d9db13ee0a154dce437bcb9d8ee5618acbec0f116a193"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.08136",
    "kind": "arxiv",
    "version": 1
  }
}