Pith Number

pith:BA3MIEAI

pith:2011:BA3MIEAIZAULLRXZYLQWI2ONYH

not attested not anchored not stored refs pending

On the Number of Pentagons in Triangle-Free Graphs

Alexander Razborov, Daniel Kr\'al, Hamed Hatami, Jan Hladk\'y, Serguei Norine

arxiv:1102.1634 v4 · 2011-02-08 · 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{BA3MIEAIZAULLRXZYLQWI2ONYH}

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	2026-05-18T00:39:18.796739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0836c41008c828b5c6f9c2e16469cdc1cc0e881ec31341a046036843b79c9a78

Aliases

arxiv: 1102.1634 · arxiv_version: 1102.1634v4 · doi: 10.48550/arxiv.1102.1634 · pith_short_12: BA3MIEAIZAUL · pith_short_16: BA3MIEAIZAULLRXZ · pith_short_8: BA3MIEAI

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/BA3MIEAIZAULLRXZYLQWI2ONYH \
  | 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: 0836c41008c828b5c6f9c2e16469cdc1cc0e881ec31341a046036843b79c9a78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a84023885a4508f1101c9056c2bf6518352bb910f21b9dbe14baa237bf930bdb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-08T16:03:59Z",
    "title_canon_sha256": "027c3f660855e331b2b196f8a111fb2f6066664770528cb982bef3d61aa93fd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1634",
    "kind": "arxiv",
    "version": 4
  }
}