Pith Number

pith:QK45ML7Q

pith:2023:QK45ML7Q2VBULM7Y5BDWBN4D5I

not attested not anchored not stored refs pending

Deflection and gravitational lensing with finite distance effect in the strong deflection limit in stationary and axisymmetric spacetimes

Junji Jia, Siyan Lin, Yujie Duan

arxiv:2304.07496 v2 · 2023-04-15 · 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{QK45ML7Q2VBULM7Y5BDWBN4D5I}

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	2026-07-05T06:32:27.227080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82b9d62ff0d54345b3f8e84760b783ea2bd1a554dc3c19d6cdd000113409ff32

Aliases

arxiv: 2304.07496 · arxiv_version: 2304.07496v2 · doi: 10.48550/arxiv.2304.07496 · pith_short_12: QK45ML7Q2VBU · pith_short_16: QK45ML7Q2VBULM7Y · pith_short_8: QK45ML7Q

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/QK45ML7Q2VBULM7Y5BDWBN4D5I \
  | 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: 82b9d62ff0d54345b3f8e84760b783ea2bd1a554dc3c19d6cdd000113409ff32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69ce6f6d916943c490a1e1f59f83fb6a5a8eb1bbeb25e8209142e3fe9fa06356",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2023-04-15T07:33:51Z",
    "title_canon_sha256": "2b43225682cb4fb3b773c3f491486fe8df6c876484de2a6f47ccb1c3dfdd2671"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2304.07496",
    "kind": "arxiv",
    "version": 2
  }
}