Pith Number

pith:BL2KQQOV

pith:2015:BL2KQQOVSZZGUYIJRCHNTSI6JC

not attested not anchored not stored refs pending

Improvements on the density of maximal 1-planar graphs

G\'eza T\'oth, J\'anos Bar\'at

arxiv:1509.05548 v1 · 2015-09-18 · 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{BL2KQQOVSZZGUYIJRCHNTSI6JC}

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	2026-05-18T01:32:42.869519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0af4a841d596726a6109888ed9c91e48a315cc97c410f7fc8ecf0a74729a68b3

Aliases

arxiv: 1509.05548 · arxiv_version: 1509.05548v1 · doi: 10.48550/arxiv.1509.05548 · pith_short_12: BL2KQQOVSZZG · pith_short_16: BL2KQQOVSZZGUYIJ · pith_short_8: BL2KQQOV

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/BL2KQQOVSZZGUYIJRCHNTSI6JC \
  | 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: 0af4a841d596726a6109888ed9c91e48a315cc97c410f7fc8ecf0a74729a68b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6c79cd1cd446ca2c13f0d3b5231b5cf662c285447a61703fcf9c63ee2f6baf6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-18T08:50:56Z",
    "title_canon_sha256": "95374c80053e06caf6aa97db2f7071f45fedf3dbef0c18deb680351c3fe33c28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05548",
    "kind": "arxiv",
    "version": 1
  }
}