Pith Number

pith:VBPFR2F4

pith:2013:VBPFR2F4IQ4IVDHREE7WLJC6IL

not attested not anchored not stored refs pending

Exact general relativistic lensing versus thin lens approximation: the crucial role of the void

Javad T. Firouzjaee, M. Parsi Mood, Reza Mansouri

arxiv:1304.5062 v1 · 2013-04-18 · 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{VBPFR2F4IQ4IVDHREE7WLJC6IL}

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	2026-05-18T03:27:41.914034Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a85e58e8bc44388a8cf1213f65a45e42d4a5001189dcbef907bb8e80a636bcc0

Aliases

arxiv: 1304.5062 · arxiv_version: 1304.5062v1 · doi: 10.48550/arxiv.1304.5062 · pith_short_12: VBPFR2F4IQ4I · pith_short_16: VBPFR2F4IQ4IVDHR · pith_short_8: VBPFR2F4

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/VBPFR2F4IQ4IVDHREE7WLJC6IL \
  | 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: a85e58e8bc44388a8cf1213f65a45e42d4a5001189dcbef907bb8e80a636bcc0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c52028777d73498cecd4218d04ec9566137a2f7a4a75638c2cbb0da06dbcb250",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2013-04-18T09:37:27Z",
    "title_canon_sha256": "a18654031e34b879df11e60e3d336b89a3398f6f01a61fbb4c1167cd32a5bff9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.5062",
    "kind": "arxiv",
    "version": 1
  }
}