Pith Number

pith:57NFVWTK

pith:2015:57NFVWTKYIUSHH4AVGPJWFI3SA

not attested not anchored not stored refs pending

Strong gravitational lensing for the photons coupled to Weyl tensor in a Schwarzschild black hole spacetime

Jiliang Jing, Songbai Chen

arxiv:1502.01088 v3 · 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{57NFVWTKYIUSHH4AVGPJWFI3SA}

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

2 papers in Pith

Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A$^*$

Photon rings and shadows of black holes with non-minimal couplings between curvature and electromagnetic field

Receipt and verification

First computed	2026-05-18T01:31:18.906772Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efda5ada6ac229239f80a99e9b151b9026c75dd07a160c86fa5938bd7e31d51b

Aliases

arxiv: 1502.01088 · arxiv_version: 1502.01088v3 · doi: 10.48550/arxiv.1502.01088 · pith_short_12: 57NFVWTKYIUS · pith_short_16: 57NFVWTKYIUSHH4A · pith_short_8: 57NFVWTK

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/57NFVWTKYIUSHH4AVGPJWFI3SA \
  | 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: efda5ada6ac229239f80a99e9b151b9026c75dd07a160c86fa5938bd7e31d51b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "936effaee7e459ca4e8e28938604d47d4a42f6d8a5a841c4f193de958ab923ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2015-02-04T04:03:13Z",
    "title_canon_sha256": "59acfc008adeb11a4d6170a0e14b967eaa728d85514bc1c63fa1a18b1ca63128"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.01088",
    "kind": "arxiv",
    "version": 3
  }
}