Pith Number

pith:5IWZ6XBL

pith:2013:5IWZ6XBL74EVPJKTJKMP7LAQBE

not attested not anchored not stored refs pending

Characterizing 2-crossing-critical graphs

Bogdan Oporowski, Drago Bokal, Gelasio Salazar, R. Bruce Richter

arxiv:1312.3712 v1 · 2013-12-13 · 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{5IWZ6XBL74EVPJKTJKMP7LAQBE}

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	2026-05-18T03:04:47.868544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea2d9f5c2bff0957a5534a98ffac100934449e8bb450e9b4f463152ad25f8116

Aliases

arxiv: 1312.3712 · arxiv_version: 1312.3712v1 · doi: 10.48550/arxiv.1312.3712 · pith_short_12: 5IWZ6XBL74EV · pith_short_16: 5IWZ6XBL74EVPJKT · pith_short_8: 5IWZ6XBL

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/5IWZ6XBL74EVPJKTJKMP7LAQBE \
  | 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: ea2d9f5c2bff0957a5534a98ffac100934449e8bb450e9b4f463152ad25f8116

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aef14aa96495989a6706e17f296a76c580d37f3d35bb1c36eca7ab2b5b778f31",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-12-13T06:31:32Z",
    "title_canon_sha256": "c558840e2b3555c595eeabd6c50354ea5746dece0d6de5e8bd2fec9cc462d732"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3712",
    "kind": "arxiv",
    "version": 1
  }
}