Pith Number

pith:OHGFAXTP

pith:2016:OHGFAXTPBCPMGWP6AONNQDBA5Y

not attested not anchored not stored refs pending

Curious case of gravitational lensing by binary black holes: a tale of two photon spheres, new relativistic images and caustics

D. Narasimha, Mandar Patil, Priti Mishra

arxiv:1610.04863 v3 · 2016-10-16 · gr-qc · astro-ph.HE · hep-th

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OHGFAXTPBCPMGWP6AONNQDBA5Y}

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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

Strong-deflection expansion of the deflection angle near a degenerate photon sphere

Receipt and verification

First computed	2026-05-18T00:52:09.124017Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71cc505e6f089ec359fe039ad80c20ee1bfb72c7014e6ae3c09b56751c8f81f5

Aliases

arxiv: 1610.04863 · arxiv_version: 1610.04863v3 · doi: 10.48550/arxiv.1610.04863 · pith_short_12: OHGFAXTPBCPM · pith_short_16: OHGFAXTPBCPMGWP6 · pith_short_8: OHGFAXTP

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/OHGFAXTPBCPMGWP6AONNQDBA5Y \
  | 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: 71cc505e6f089ec359fe039ad80c20ee1bfb72c7014e6ae3c09b56751c8f81f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8968def9764c0e9bfd6961b96e79bda84b47682c9710f5c2ec35a36d1493e585",
    "cross_cats_sorted": [
      "astro-ph.HE",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2016-10-16T14:14:47Z",
    "title_canon_sha256": "adbbb95bcf63a7ad9df9a4290ae8a8bedc39f1acfbab039a251fee10fd9dce87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.04863",
    "kind": "arxiv",
    "version": 3
  }
}