Pith Number

pith:5QQ346EC

pith:2015:5QQ346ECJFQU64YRSX7MFOWUGK

not attested not anchored not stored refs pending

Strong Gravitational Lensing by Kiselev Black Hole

Azka Younas, Mubasher Jamil, Saqib Hussain, Sebastian Bahamonde

arxiv:1502.01676 v5 · 2015-02-04 · 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{5QQ346ECJFQU64YRSX7MFOWUGK}

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	2026-05-18T01:29:46.548648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec21be788249614f731195fec2bad432b013920980c034b0da83fb2e925e52e6

Aliases

arxiv: 1502.01676 · arxiv_version: 1502.01676v5 · doi: 10.48550/arxiv.1502.01676 · pith_short_12: 5QQ346ECJFQU · pith_short_16: 5QQ346ECJFQU64YR · pith_short_8: 5QQ346EC

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/5QQ346ECJFQU64YRSX7MFOWUGK \
  | 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: ec21be788249614f731195fec2bad432b013920980c034b0da83fb2e925e52e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f3cfad60394990921f9df0f83be0553124a89d30f02704f9ca4eee073d94e2c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2015-02-04T10:54:39Z",
    "title_canon_sha256": "f0f9c4d1545a419ef6086fceb67f814f221fde209da417f778ae204acafc7c84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.01676",
    "kind": "arxiv",
    "version": 5
  }
}