Pith Number

pith:3P5VK2AL

pith:2015:3P5VK2ALZWAIAFV2UTZQXGAVTC

not attested not anchored not stored refs pending

Strong Gravitational Lensing in a Brane-World Black Hole

Biao Cao, Guoping Li, Xiaotao Zu, Zhongwen Feng

arxiv:1506.08410 v1 · 2015-06-28 · 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{3P5VK2ALZWAIAFV2UTZQXGAVTC}

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	2026-05-18T01:37:45.384912Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbfb55680bcd808016baa4f30b981598816e8516b4292e18385cd39c6af117ac

Aliases

arxiv: 1506.08410 · arxiv_version: 1506.08410v1 · doi: 10.48550/arxiv.1506.08410 · pith_short_12: 3P5VK2ALZWAI · pith_short_16: 3P5VK2ALZWAIAFV2 · pith_short_8: 3P5VK2AL

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/3P5VK2ALZWAIAFV2UTZQXGAVTC \
  | 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: dbfb55680bcd808016baa4f30b981598816e8516b4292e18385cd39c6af117ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "804c468b18b134eabb05e895d73a8df107db3c6dd0d06826ea22f83b93a71cdc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2015-06-28T14:55:21Z",
    "title_canon_sha256": "3985480e28da4be5e2a8dab0205acb43963f38d84972fe3d45a8cc206e7d3b35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.08410",
    "kind": "arxiv",
    "version": 1
  }
}