Pith Number

pith:NHXKSBWY

pith:2011:NHXKSBWYOVB6XMQT5AMUJRDMMN

not attested not anchored not stored refs pending

Longest cycles in sparse random digraphs

Benny Sudakov, Eyal Lubetzky, Michael Krivelevich

arxiv:1102.3147 v1 · 2011-02-15 · 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{NHXKSBWYOVB6XMQT5AMUJRDMMN}

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	2026-05-18T04:28:38.326727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69eea906d87543ebb213e81944c46c637c11c199646558e55259535787f68d7f

Aliases

arxiv: 1102.3147 · arxiv_version: 1102.3147v1 · doi: 10.48550/arxiv.1102.3147 · pith_short_12: NHXKSBWYOVB6 · pith_short_16: NHXKSBWYOVB6XMQT · pith_short_8: NHXKSBWY

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/NHXKSBWYOVB6XMQT5AMUJRDMMN \
  | 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: 69eea906d87543ebb213e81944c46c637c11c199646558e55259535787f68d7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a242e3291f8aeeeff77ffdf4d93b614f5ae2c4ae2cfa086f5711de2c4aa1817",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-15T18:22:19Z",
    "title_canon_sha256": "9e72a5360bf56f374a0a5250ad90d213886712d13c32913398d64912a53dc084"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.3147",
    "kind": "arxiv",
    "version": 1
  }
}