Pith Number

pith:7PXZWHD2

pith:2013:7PXZWHD2V7U7AABBK3LUNKNGSN

not attested not anchored not stored refs pending

The triangle-free graphs with rank 6

Long Wang, Yi Wang, Yi-Zheng Fan

arxiv:1301.0374 v2 · 2013-01-03 · 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{7PXZWHD2V7U7AABBK3LUNKNGSN}

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	2026-05-18T02:42:37.503858Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbef9b1c7aafe9f0002156d746a9a6936d5fa9f0d6daa66c40c09e9a4c6ff46f

Aliases

arxiv: 1301.0374 · arxiv_version: 1301.0374v2 · doi: 10.48550/arxiv.1301.0374 · pith_short_12: 7PXZWHD2V7U7 · pith_short_16: 7PXZWHD2V7U7AABB · pith_short_8: 7PXZWHD2

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/7PXZWHD2V7U7AABBK3LUNKNGSN \
  | 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: fbef9b1c7aafe9f0002156d746a9a6936d5fa9f0d6daa66c40c09e9a4c6ff46f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e2f12fdbd27c7293092ec1885a8b9cc74f6f02ce3bafa0573d7b7a1b7bd0b6e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-01-03T04:15:19Z",
    "title_canon_sha256": "455bdb681e7f8c63e38ad0fdf95582bd99c23fedee3af6501c3bb771b9903c04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.0374",
    "kind": "arxiv",
    "version": 2
  }
}