Pith Number

pith:OXTBJAOP

pith:2015:OXTBJAOPQJUZXF4UIURZCEE5BI

not attested not anchored not stored refs pending

On the Planar Split Thickness of Graphs

Anna Lubiw, Aude Maignan, David Eppstein, Debajyoti Mondal, Giuseppe Liotta, Hamideh Vosoughpour, Philipp Kindermann, Stephen Kobourov, Stephen Wismath, Sue Whitesides

arxiv:1512.04839 v4 · 2015-12-15 · 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{OXTBJAOPQJUZXF4UIURZCEE5BI}

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	2026-05-18T00:23:17.321811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

75e61481cf82699b9794452391109d0a36532abc839ba09c6dba749d65bd6fa1

Aliases

arxiv: 1512.04839 · arxiv_version: 1512.04839v4 · doi: 10.48550/arxiv.1512.04839 · pith_short_12: OXTBJAOPQJUZ · pith_short_16: OXTBJAOPQJUZXF4U · pith_short_8: OXTBJAOP

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/OXTBJAOPQJUZXF4UIURZCEE5BI \
  | 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: 75e61481cf82699b9794452391109d0a36532abc839ba09c6dba749d65bd6fa1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c8455b3aa4e95ac1f13377e24250b4d30c0a6dd56d295846eca09e0d16fa3ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-15T16:19:00Z",
    "title_canon_sha256": "07b07681fc5990b9b60a116fcb2453fb57c734d368c482a030e5f6f26f02ec6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04839",
    "kind": "arxiv",
    "version": 4
  }
}