Pith Number

pith:ZADDWDG7

pith:2010:ZADDWDG76EL5CQQBU5LJ2HPYMH

not attested not anchored not stored refs pending

Mass Function of Rich Galaxy Clusters and Its Constraint on sigma_8

F. S. Liu, J. L. Han, Z. L. Wen

arxiv:1004.3337 v2 · 2010-04-20 · astro-ph.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{ZADDWDG76EL5CQQBU5LJ2HPYMH}

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	2026-05-18T02:07:56.469472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8063b0cdff117d14201a7569d1df861c1289c89afb82188a970920d5c4d69cc

Aliases

arxiv: 1004.3337 · arxiv_version: 1004.3337v2 · doi: 10.48550/arxiv.1004.3337 · pith_short_12: ZADDWDG76EL5 · pith_short_16: ZADDWDG76EL5CQQB · pith_short_8: ZADDWDG7

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/ZADDWDG76EL5CQQBU5LJ2HPYMH \
  | 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: c8063b0cdff117d14201a7569d1df861c1289c89afb82188a970920d5c4d69cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc2ab216028c0b99ce7181829d679b0499e78aa15c1fe8e87a7351e0a2971496",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2010-04-20T03:46:37Z",
    "title_canon_sha256": "dac6605b027059907841bf4b01bb18d8e95a1b568422fd78bfa03395ebbb4486"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.3337",
    "kind": "arxiv",
    "version": 2
  }
}