Pith Number

pith:PEEVL4NW

pith:2013:PEEVL4NW43O5HZKSUDARE2DRUW

not attested not anchored not stored refs pending

Planar 4-critical graphs with four triangles

Alexandr V. Kostochka, Bernard Lidick\'y, Matthew Yancey, Oleg V. Borodin, Zden\v{e}k Dvo\v{r}\'ak

arxiv:1306.1477 v1 · 2013-06-06 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PEEVL4NW43O5HZKSUDARE2DRUW}

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	2026-05-18T00:54:58.416166Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

790955f1b6e6ddd3e552a0c1126871a5a1cd443eb2ba80bf48aa1ae044c884fd

Aliases

arxiv: 1306.1477 · arxiv_version: 1306.1477v1 · doi: 10.48550/arxiv.1306.1477 · pith_short_12: PEEVL4NW43O5 · pith_short_16: PEEVL4NW43O5HZKS · pith_short_8: PEEVL4NW

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/PEEVL4NW43O5HZKSUDARE2DRUW \
  | 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: 790955f1b6e6ddd3e552a0c1126871a5a1cd443eb2ba80bf48aa1ae044c884fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abe610e455d2a87729b6f1a58d9feeae646758b828ed75245b62c4fe34847dea",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-06-06T17:12:30Z",
    "title_canon_sha256": "d0fb24a0a83f633261496ddff6c15e17ebbf1771c9b3063b2529727bcf9c83ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1477",
    "kind": "arxiv",
    "version": 1
  }
}