Pith Number

pith:UJX5GCDB

pith:2005:UJX5GCDBTQQ6ITGGO44Q2CTVEF

not attested not anchored not stored refs pending

The phase transition in inhomogeneous random graphs

Bela Bollobas, Oliver Riordan, Svante Janson

arxiv:math/0504589 v3 · 2005-04-29 · 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{UJX5GCDBTQQ6ITGGO44Q2CTVEF}

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	2026-05-18T04:08:35.690952Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a26fd308619c21e44cc677390d0a75215c85f259eae7966597a1f988502ce819

Aliases

arxiv: math/0504589 · arxiv_version: math/0504589v3 · doi: 10.48550/arxiv.math/0504589 · pith_short_12: UJX5GCDBTQQ6 · pith_short_16: UJX5GCDBTQQ6ITGG · pith_short_8: UJX5GCDB

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/UJX5GCDBTQQ6ITGGO44Q2CTVEF \
  | 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: a26fd308619c21e44cc677390d0a75215c85f259eae7966597a1f988502ce819

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2ed954a570c8b254b7482a522d44f2e294485e525efd5a39de290133e9cf616",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-04-29T09:21:30Z",
    "title_canon_sha256": "7ab5744283565a084c906a9d34c08ef294af273d99d6fb0ebc8fc27123546469"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0504589",
    "kind": "arxiv",
    "version": 3
  }
}