Pith Number

pith:PI7LCMB5

pith:2021:PI7LCMB5K23NQMFM7KMG6M4QVQ

not attested not anchored not stored refs pending

Gravitational lensing by a photon sphere in a Reissner-Nordstr\"{o}m naked singularity spacetime in strong deflection limits

Naoki Tsukamoto

arxiv:2107.07146 v5 · 2021-07-15 · 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{PI7LCMB5K23NQMFM7KMG6M4QVQ}

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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	2026-07-05T03:37:27.050405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a3eb1303d56b6d830acfa986f3390ac0eae4d9d5e4e708b8a763ec27be99aaf

Aliases

arxiv: 2107.07146 · arxiv_version: 2107.07146v5 · doi: 10.48550/arxiv.2107.07146 · pith_short_12: PI7LCMB5K23N · pith_short_16: PI7LCMB5K23NQMFM · pith_short_8: PI7LCMB5

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/PI7LCMB5K23NQMFM7KMG6M4QVQ \
  | 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: 7a3eb1303d56b6d830acfa986f3390ac0eae4d9d5e4e708b8a763ec27be99aaf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f248a2182a0748529c0925b691a0edb783cc6ebaac1396d114cafaf109fa0865",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-07-15T06:21:48Z",
    "title_canon_sha256": "01ff62aeaf83dbe73e66fe592e3241649f786a8fa235e70e1ac7a35f3e70d202"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.07146",
    "kind": "arxiv",
    "version": 5
  }
}