Pith Number

pith:Z7QLBDF3

pith:2014:Z7QLBDF3CK2AMDWNOQXUOJBWOE

not attested not anchored not stored refs pending

The Raychaudhuri equation in homogeneous cosmologies

A. de la Cruz-Dombriz, A. Dobado, F. D. Albareti, J. A. R. Cembranos

arxiv:1401.7926 v2 · 2014-01-30 · 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{Z7QLBDF3CK2AMDWNOQXUOJBWOE}

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	2026-05-18T02:56:12.417893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfe0b08cbb12b4060ecd742f472436713247437e8089574f3957a30da96a44f5

Aliases

arxiv: 1401.7926 · arxiv_version: 1401.7926v2 · doi: 10.48550/arxiv.1401.7926 · pith_short_12: Z7QLBDF3CK2A · pith_short_16: Z7QLBDF3CK2AMDWN · pith_short_8: Z7QLBDF3

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/Z7QLBDF3CK2AMDWNOQXUOJBWOE \
  | 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: cfe0b08cbb12b4060ecd742f472436713247437e8089574f3957a30da96a44f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa9ec8d6773583ed70085673852615bffa600400412997995aef9d9b15f0f058",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2014-01-30T17:16:39Z",
    "title_canon_sha256": "27cc8f0ab205be82fdfc80012722697f461be4e52d27173e7c4d8352fc2a1b81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.7926",
    "kind": "arxiv",
    "version": 2
  }
}