Pith Number

pith:K5D3EQTZ

pith:2015:K5D3EQTZ2EXRJWZ4REDSJEJ2FQ

not attested not anchored not stored refs pending

The typical structure of maximal triangle-free graphs

Hong Liu, J\'ozsef Balogh, Maryam Sharifzadeh, \v{S}\'arka Pet\v{r}\'i\v{c}kov\'a

arxiv:1501.02849 v1 · 2015-01-12 · 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{K5D3EQTZ2EXRJWZ4REDSJEJ2FQ}

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	2026-05-18T01:09:51.033891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5747b24279d12f14db3c890724913a2c3c8d6957778e29938bd45557d8c33cee

Aliases

arxiv: 1501.02849 · arxiv_version: 1501.02849v1 · doi: 10.48550/arxiv.1501.02849 · pith_short_12: K5D3EQTZ2EXR · pith_short_16: K5D3EQTZ2EXRJWZ4 · pith_short_8: K5D3EQTZ

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/K5D3EQTZ2EXRJWZ4REDSJEJ2FQ \
  | 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: 5747b24279d12f14db3c890724913a2c3c8d6957778e29938bd45557d8c33cee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d70b71063b08a13d988a836133a2a732e24f0cd893722cd42e0435583027c25",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-01-12T23:26:08Z",
    "title_canon_sha256": "5353e78408343b712374dbf7fae3b373d8118fa0b8d6d15abe17b366a70abfc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.02849",
    "kind": "arxiv",
    "version": 1
  }
}