Pith Number

pith:27BEGI4I

pith:2012:27BEGI4ISEFNYFGYJKBLQDPFTU

not attested not anchored not stored refs pending

A central limit theorem in the $\beta$-model for undirected random graphs with a diverging number of vertices

Jinfeng Xu, Ting Yan

arxiv:1202.3307 v3 · 2012-02-15 · math.ST · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{27BEGI4ISEFNYFGYJKBLQDPFTU}

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	2026-05-18T03:19:35.417373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7c2432388910adc14d84a82b80de59d243ae4379c8043a7f65614b568f818bd

Aliases

arxiv: 1202.3307 · arxiv_version: 1202.3307v3 · doi: 10.48550/arxiv.1202.3307 · pith_short_12: 27BEGI4ISEFN · pith_short_16: 27BEGI4ISEFNYFGY · pith_short_8: 27BEGI4I

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/27BEGI4ISEFNYFGYJKBLQDPFTU \
  | 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: d7c2432388910adc14d84a82b80de59d243ae4379c8043a7f65614b568f818bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37702df68cede91168a7aae5a235d431c5a40f58bb4af1f909296c263c1c9093",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2012-02-15T14:08:36Z",
    "title_canon_sha256": "509eeab1160b8154ebff869f7603873a3120da2e296768e9a8d2246e01c8b8cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3307",
    "kind": "arxiv",
    "version": 3
  }
}