Pith Number

pith:6Y2LASGA

pith:2016:6Y2LASGAHKAA6QJ3LNVM3T2P7C

not attested not anchored not stored refs pending

A Quantitative Local Limit Theorem for Triangles in Random Graphs

Ross Berkowitz

arxiv:1610.01281 v3 · 2016-10-05 · 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{6Y2LASGAHKAA6QJ3LNVM3T2P7C}

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	2026-05-18T00:48:16.876184Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f634b048c03a800f413b5b6acdcf4ff892ed6bb71dce8b162e238ab5c34ec409

Aliases

arxiv: 1610.01281 · arxiv_version: 1610.01281v3 · doi: 10.48550/arxiv.1610.01281 · pith_short_12: 6Y2LASGAHKAA · pith_short_16: 6Y2LASGAHKAA6QJ3 · pith_short_8: 6Y2LASGA

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/6Y2LASGAHKAA6QJ3LNVM3T2P7C \
  | 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: f634b048c03a800f413b5b6acdcf4ff892ed6bb71dce8b162e238ab5c34ec409

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9260a5031d21905f6d7d438c69095b81dc8a900916d3a084263f389071140411",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-10-05T06:34:02Z",
    "title_canon_sha256": "179b8e91d0610ebce2761a977891d15e7694c2b05d3e3d4d67f867daf7cd4320"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.01281",
    "kind": "arxiv",
    "version": 3
  }
}