Pith Number

pith:GE2ADHN5

pith:2009:GE2ADHN5BW7NNMNQ6VEQDFBSR2

not attested not anchored not stored refs pending

Crossing-critical graphs with large maximum degree

Bojan Mohar, Zdenek Dvorak

arxiv:0907.1599 v1 · 2009-07-09 · 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{GE2ADHN5BW7NNMNQ6VEQDFBSR2}

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	2026-05-18T04:31:42.318237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3134019dbd0dbed6b1b0f5490194328eac6feab871efb46e0f16f7cc7f1420d5

Aliases

arxiv: 0907.1599 · arxiv_version: 0907.1599v1 · doi: 10.48550/arxiv.0907.1599 · pith_short_12: GE2ADHN5BW7N · pith_short_16: GE2ADHN5BW7NNMNQ · pith_short_8: GE2ADHN5

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/GE2ADHN5BW7NNMNQ6VEQDFBSR2 \
  | 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: 3134019dbd0dbed6b1b0f5490194328eac6feab871efb46e0f16f7cc7f1420d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6ef51cb9f6ffe752fe67f84454baf5d37284d3897744f017f5d693019544d88",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-07-09T16:04:34Z",
    "title_canon_sha256": "3c48d4cc4e99882eed89b64badd3c5ee506947acdd9690fe331b6c4dac7bf4f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.1599",
    "kind": "arxiv",
    "version": 1
  }
}