Pith Number

pith:ROFFFGPA

pith:2010:ROFFFGPAZVJJ3HXLGBQVDM223V

not attested not anchored not stored refs pending

Raychaudhuri's equation and aspects of relativistic charged collapse

Alexandros P. Kouretsis, Christos G. Tsagas

arxiv:1010.4211 v2 · 2010-10-20 · gr-qc · 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{ROFFFGPAZVJJ3HXLGBQVDM223V}

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	2026-05-18T04:31:32.070652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b8a5299e0cd529d9eeb306151b35add78304f720d1287d220377f0ef088662b

Aliases

arxiv: 1010.4211 · arxiv_version: 1010.4211v2 · doi: 10.48550/arxiv.1010.4211 · pith_short_12: ROFFFGPAZVJJ · pith_short_16: ROFFFGPAZVJJ3HXL · pith_short_8: ROFFFGPA

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/ROFFFGPAZVJJ3HXLGBQVDM223V \
  | 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: 8b8a5299e0cd529d9eeb306151b35add78304f720d1287d220377f0ef088662b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5bc01aef443997ca118d2ac834fbc14bc5283e898574cba26a154d8396282938",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2010-10-20T14:22:31Z",
    "title_canon_sha256": "9efeff5ea84b385d3b21547af4a7a2b2511b60039ffb9d5f502d1ae20d11f97e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4211",
    "kind": "arxiv",
    "version": 2
  }
}