Pith Number

pith:7MNXWCVS

pith:2013:7MNXWCVSDTCE4JIYLYCZ45E3QX

not attested not anchored not stored refs pending

Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk

Daniel Kral, Robin Thomas, Zdenek Dvorak

arxiv:1302.2158 v4 · 2013-02-08 · 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{7MNXWCVSDTCE4JIYLYCZ45E3QX}

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	2026-05-18T00:40:52.185127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb1b7b0ab21cc44e25185e059e749b85e9a0df3a2c9a169864dbdb7fc412668f

Aliases

arxiv: 1302.2158 · arxiv_version: 1302.2158v4 · doi: 10.48550/arxiv.1302.2158 · pith_short_12: 7MNXWCVSDTCE · pith_short_16: 7MNXWCVSDTCE4JIY · pith_short_8: 7MNXWCVS

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/7MNXWCVSDTCE4JIYLYCZ45E3QX \
  | 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: fb1b7b0ab21cc44e25185e059e749b85e9a0df3a2c9a169864dbdb7fc412668f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4bd440982cddcdfb252b004c7120f35851b97d5f08afd4e51a0b5ef684b4b3f4",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-08T21:25:22Z",
    "title_canon_sha256": "131a0ea3f327d6f46fb3858257fbadcae8d5c9ae64cb7a3607ad3e70691e2d88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.2158",
    "kind": "arxiv",
    "version": 4
  }
}