Pith Number

pith:FCF4VAEQ

pith:2013:FCF4VAEQPSFSAKU2P65DQLXL3Y

not attested not anchored not stored refs pending

Strong gravitational lensing in a black-hole spacetime dominated by dark energy

Changqing Liu, Chikun Ding, Liqun Jiang, Rong-Gen Cai, Yuanyuan Xiao

arxiv:1308.5035 v2 · 2013-08-23 · 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{FCF4VAEQPSFSAKU2P65DQLXL3Y}

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.

Cited by

1 paper in Pith

Time Like Geodesics of Regular Black Holes with Scalar Hair

Receipt and verification

First computed	2026-05-18T03:07:13.899550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

288bca80907c8b202a9a7fba382eebde1c8c37f6d10c30a54749edafb1adad11

Aliases

arxiv: 1308.5035 · arxiv_version: 1308.5035v2 · doi: 10.48550/arxiv.1308.5035 · pith_short_12: FCF4VAEQPSFS · pith_short_16: FCF4VAEQPSFSAKU2 · pith_short_8: FCF4VAEQ

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/FCF4VAEQPSFSAKU2P65DQLXL3Y \
  | 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: 288bca80907c8b202a9a7fba382eebde1c8c37f6d10c30a54749edafb1adad11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "896282ee1b31a976f2460df23bc1bfb6323c9559ab7a09fbbb8dd2297df40e09",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2013-08-23T03:26:25Z",
    "title_canon_sha256": "c2a5f0318b5aa378ec43d748fa2f895d60859a38a9b0b0751f77c41be7a9037d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.5035",
    "kind": "arxiv",
    "version": 2
  }
}