Pith Number

pith:HGB4FHNG

pith:2013:HGB4FHNGW4BYLD2W2WCGC7YTIM

not attested not anchored not stored refs pending

New bounds on the maximum number of edges in $k$-quasi-planar graphs

Andrew Suk, Bartosz Walczak

arxiv:1309.0395 v3 · 2013-09-02 · math.CO · 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{HGB4FHNGW4BYLD2W2WCGC7YTIM}

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	2026-05-18T01:21:49.547457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3983c29da6b703858f56d584617f1343072566a05fb254255b0d789bfdfb7cc1

Aliases

arxiv: 1309.0395 · arxiv_version: 1309.0395v3 · doi: 10.48550/arxiv.1309.0395 · pith_short_12: HGB4FHNGW4BY · pith_short_16: HGB4FHNGW4BYLD2W · pith_short_8: HGB4FHNG

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/HGB4FHNGW4BYLD2W2WCGC7YTIM \
  | 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: 3983c29da6b703858f56d584617f1343072566a05fb254255b0d789bfdfb7cc1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "825dfd5acd090d282249e47f6826a8f1a199112dccc48a9578c84bb2242e7dcb",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-02T13:06:38Z",
    "title_canon_sha256": "f003ff271a58b76a0a4db5477545bd18da5c5874ec1f20eaae3e6d222a87a3ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0395",
    "kind": "arxiv",
    "version": 3
  }
}