Pith Number

pith:QIQPDRHE

pith:2012:QIQPDRHEAOBWVLEI3SHU7HTGFU

not attested not anchored not stored refs pending

Relativistic Cosmology Number Densities and the Luminosity Function

(2) Physics Institute, (3) Vatican Observatory Group, Alvaro S. Iribarrem (1), Amanda R. Lopes (1), Brazil, Federal University of Rio de Janeiro - UFRJ, Marcelo B. Ribeiro (2), Steward Observatory, Tucson, University of Arizona, USA), William R. Stoeger (3) ((1) Valongo Observatory

arxiv:1201.5571 v2 · 2012-01-26 · astro-ph.CO · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QIQPDRHEAOBWVLEI3SHU7HTGFU}

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	2026-05-18T04:01:01.412403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8220f1c4e403836aac88dc8f4f9e662d09c05999e7ad13a003e3ed839cea227a

Aliases

arxiv: 1201.5571 · arxiv_version: 1201.5571v2 · doi: 10.48550/arxiv.1201.5571 · pith_short_12: QIQPDRHEAOBW · pith_short_16: QIQPDRHEAOBWVLEI · pith_short_8: QIQPDRHE

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/QIQPDRHEAOBWVLEI3SHU7HTGFU \
  | 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: 8220f1c4e403836aac88dc8f4f9e662d09c05999e7ad13a003e3ed839cea227a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b177546e95705f8588e7c87789079e12a137937c41e910246a0afd0e318a281a",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2012-01-26T16:30:31Z",
    "title_canon_sha256": "f7b2369a4edea45d0da36597223839f63613c688400e9ffa21f7a4ba5a8ee273"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.5571",
    "kind": "arxiv",
    "version": 2
  }
}