Pith Number

pith:VKZ5TXZQ

pith:2012:VKZ5TXZQ7KVLRUET5C5RT426HJ

not attested not anchored not stored refs pending

Tur\'an H-densities for 3-graphs

Emil R. Vaughan, Victor Falgas-Ravry

arxiv:1201.4326 v1 · 2012-01-20 · 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{VKZ5TXZQ7KVLRUET5C5RT426HJ}

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	2026-05-18T02:25:11.244963Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aab3d9df30faaab8d093e8bb19f35e3a75130b606068be6605d8d6382ee66697

Aliases

arxiv: 1201.4326 · arxiv_version: 1201.4326v1 · doi: 10.48550/arxiv.1201.4326 · pith_short_12: VKZ5TXZQ7KVL · pith_short_16: VKZ5TXZQ7KVLRUET · pith_short_8: VKZ5TXZQ

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/VKZ5TXZQ7KVLRUET5C5RT426HJ \
  | 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: aab3d9df30faaab8d093e8bb19f35e3a75130b606068be6605d8d6382ee66697

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b14930d2fa8a7db74872a78ab2bb025cb26a7c4b6813b780a27aadd3a7e81ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-01-20T16:02:34Z",
    "title_canon_sha256": "40fe4c88bda62f944571f549d299691d20a03d06618c6221630f4835cc13d102"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4326",
    "kind": "arxiv",
    "version": 1
  }
}