Pith Number

pith:RPUH37JL

pith:2021:RPUH37JLPCAUXSAAFMBY3EXMTT

not attested not anchored not stored refs pending

Gravitational lensing by two photon spheres in a black-bounce spacetime in strong deflection limits

Naoki Tsukamoto

arxiv:2105.14336 v4 · 2021-05-29 · 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{RPUH37JLPCAUXSAAFMBY3EXMTT}

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

Three dimensional black bounces in $f(R)$ gravity

Receipt and verification

First computed	2026-07-05T03:56:29.480830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8be87dfd2b78814bc8002b038d92ec9cea7f1f709880b0690158efca73981a25

Aliases

arxiv: 2105.14336 · arxiv_version: 2105.14336v4 · doi: 10.48550/arxiv.2105.14336 · pith_short_12: RPUH37JLPCAU · pith_short_16: RPUH37JLPCAUXSAA · pith_short_8: RPUH37JL

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/RPUH37JLPCAUXSAAFMBY3EXMTT \
  | 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: 8be87dfd2b78814bc8002b038d92ec9cea7f1f709880b0690158efca73981a25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "340724c1e7464b51e6359d7f6372e525253d04c3d817a9af39b608369dfb720a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-05-29T16:35:06Z",
    "title_canon_sha256": "cef4000a5b3d43084c921e3dcfa25f96b7503bef41b1922e4da75e5e97f293a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.14336",
    "kind": "arxiv",
    "version": 4
  }
}