Pith Number

pith:ZWW23ZAZ

pith:2013:ZWW23ZAZNCUT2BVD2XBXA6NEV6

not attested not anchored not stored refs pending

The importance sampling technique for understanding rare events in Erd\H{o}s-R\'enyi random graphs

Chia Ying Lee, James Nolen, Jan Hannig, Shankar Bhamidi

arxiv:1302.6551 v2 · 2013-02-26 · math.PR · 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{ZWW23ZAZNCUT2BVD2XBXA6NEV6}

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	2026-05-18T02:55:04.279921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdadade41968a93d06a3d5c37079a4af8b527898aa12796b104fc7386e1cc6e5

Aliases

arxiv: 1302.6551 · arxiv_version: 1302.6551v2 · doi: 10.48550/arxiv.1302.6551 · pith_short_12: ZWW23ZAZNCUT · pith_short_16: ZWW23ZAZNCUT2BVD · pith_short_8: ZWW23ZAZ

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/ZWW23ZAZNCUT2BVD2XBXA6NEV6 \
  | 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: cdadade41968a93d06a3d5c37079a4af8b527898aa12796b104fc7386e1cc6e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37838e26647bbdf37e73d5dd63dad2c00f5f4b72493c7d116ce164c2e5c6618d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-02-26T19:32:21Z",
    "title_canon_sha256": "e5e7e4f8611c8e911592381889e38126296e6b7382c70eb9443fe7aaaa39f4f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.6551",
    "kind": "arxiv",
    "version": 2
  }
}