Pith Number

pith:JTMUB7S3

pith:2018:JTMUB7S3OEWUT32BL77H5JS64H

not attested not anchored not stored refs pending

Strong gravitational lensing for black hole with scalar charge in massive gravity

Jiliang Jing, Ruanjing Zhang, Songbai Chen

arxiv:1805.02330 v1 · 2018-05-07 · gr-qc · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JTMUB7S3OEWUT32BL77H5JS64H}

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

Boundary-only weak deflection angles from isothermal optical geometry

Receipt and verification

First computed	2026-05-18T00:15:54.154996Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4cd940fe5b712d49ef415ffe7ea65ee1f7d9e3320b75da6a4c58e6ddd87f9844

Aliases

arxiv: 1805.02330 · arxiv_version: 1805.02330v1 · doi: 10.48550/arxiv.1805.02330 · pith_short_12: JTMUB7S3OEWU · pith_short_16: JTMUB7S3OEWUT32B · pith_short_8: JTMUB7S3

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/JTMUB7S3OEWUT32BL77H5JS64H \
  | 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: 4cd940fe5b712d49ef415ffe7ea65ee1f7d9e3320b75da6a4c58e6ddd87f9844

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bcf2d8ae52d84b518f853f1e08116c9b3064d3e36276734ba287839552430d7",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2018-05-07T03:17:08Z",
    "title_canon_sha256": "4e185f15b903fd4ee539e7fbf2083cfc28211c620be2d7e491fd27dcc791031c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.02330",
    "kind": "arxiv",
    "version": 1
  }
}