Pith Number

pith:WGFJBMRA

pith:2010:WGFJBMRAMZ2IQWVH5QPVBGKV6G

not attested not anchored not stored refs pending

Phase transitions for modified Erd\"os-R\'enyi processes

Joel Spencer, Svante Janson

arxiv:1005.4494 v1 · 2010-05-25 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WGFJBMRAMZ2IQWVH5QPVBGKV6G}

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	2026-05-18T02:07:14.820253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b18a90b2206674885aa7ec1f509955f1af6d094722206634f37f8e1506a49014

Aliases

arxiv: 1005.4494 · arxiv_version: 1005.4494v1 · doi: 10.48550/arxiv.1005.4494 · pith_short_12: WGFJBMRAMZ2I · pith_short_16: WGFJBMRAMZ2IQWVH · pith_short_8: WGFJBMRA

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/WGFJBMRAMZ2IQWVH5QPVBGKV6G \
  | 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: b18a90b2206674885aa7ec1f509955f1af6d094722206634f37f8e1506a49014

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "559c6834ddcc8fb70151f54312e0054648245b108ca33aa1dc70f08b41d3fa4f",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-05-25T07:34:09Z",
    "title_canon_sha256": "c027d1cd6d86c462ad42df992b621a0ddc0bc872dfd4cd0bf3cea81700fae570"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.4494",
    "kind": "arxiv",
    "version": 1
  }
}