Pith Number

pith:QJ3ILZHU

pith:2015:QJ3ILZHU7ULPZEYG3M3U34QE3C

not attested not anchored not stored refs pending

The 3-colorability of planar graphs without cycles of length 4, 6 and 9

Ligang Jin, Yingli Kang, Yingqian Wang

arxiv:1506.04629 v1 · 2015-06-15 · 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{QJ3ILZHU7ULPZEYG3M3U34QE3C}

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	2026-05-18T00:50:07.083787Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

827685e4f4fd16fc9306db374df204d8b49e2d3a6238da86516943d2d3bf3cd9

Aliases

arxiv: 1506.04629 · arxiv_version: 1506.04629v1 · doi: 10.48550/arxiv.1506.04629 · pith_short_12: QJ3ILZHU7ULP · pith_short_16: QJ3ILZHU7ULPZEYG · pith_short_8: QJ3ILZHU

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/QJ3ILZHU7ULPZEYG3M3U34QE3C \
  | 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: 827685e4f4fd16fc9306db374df204d8b49e2d3a6238da86516943d2d3bf3cd9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23f698e3420d3d6870d2c21f036aae4202e50612e75cf5445c01ac8d6a0c0347",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-06-15T15:20:03Z",
    "title_canon_sha256": "7da8cdc97dbcc0df4dcd58b323ab07b32433c45082af68c17ec6c2595ee8a248"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.04629",
    "kind": "arxiv",
    "version": 1
  }
}