Pith Number

pith:ZUFDLY4C

pith:2008:ZUFDLY4CPFMB4CCIVKQS7PIH25

not attested not anchored not stored refs pending

The probability distribution of cluster formation times and implied Einstein Radii

S. Sadeh, Y. Rephaeli

arxiv:0804.0892 v1 · 2008-04-06 · astro-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZUFDLY4CPFMB4CCIVKQS7PIH25}

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	2026-07-04T17:10:14.216179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd0a35e38279581e0848aaa12fbd07d768785c74fe83216f98bc12fbe199b105

Aliases

arxiv: 0804.0892 · arxiv_version: 0804.0892v1 · doi: 10.48550/arxiv.0804.0892 · pith_short_12: ZUFDLY4CPFMB · pith_short_16: ZUFDLY4CPFMB4CCI · pith_short_8: ZUFDLY4C

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/ZUFDLY4CPFMB4CCIVKQS7PIH25 \
  | 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: cd0a35e38279581e0848aaa12fbd07d768785c74fe83216f98bc12fbe199b105

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2cfbc5c7a58b43e1fcd26a115fb0d610ea070ea398d4af3d82eb5ca0565874ad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph",
    "submitted_at": "2008-04-06T07:32:40Z",
    "title_canon_sha256": "8a895e392fc6766d446ba6e15e4ea45f606f6231cc49449ce65f80710d9fef1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0804.0892",
    "kind": "arxiv",
    "version": 1
  }
}