Pith Number

pith:F4R3PCFO

pith:2022:F4R3PCFO7SIUNRMTIE6K4HT5JG

not attested not anchored not stored refs pending

Retrolensing by two photon spheres of a black-bounce spacetime

Naoki Tsukamoto

arxiv:2202.09641 v2 · 2022-02-19 · 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{F4R3PCFO7SIUNRMTIE6K4HT5JG}

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

4 papers in Pith

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

Photon Spheres and shadow of modified black-hole entropies

Receipt and verification

First computed	2026-07-05T04:16:39.870611Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f23b788aefc9146c593413cae1e7d498c2088c98f592d8050ddfa4e89488978

Aliases

arxiv: 2202.09641 · arxiv_version: 2202.09641v2 · doi: 10.48550/arxiv.2202.09641 · pith_short_12: F4R3PCFO7SIU · pith_short_16: F4R3PCFO7SIUNRMT · pith_short_8: F4R3PCFO

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/F4R3PCFO7SIUNRMTIE6K4HT5JG \
  | 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: 2f23b788aefc9146c593413cae1e7d498c2088c98f592d8050ddfa4e89488978

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "873604026df3bfb5ef56f209480da2be5397e1c35af256dbd5f37caaa2efb35b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2022-02-19T16:58:07Z",
    "title_canon_sha256": "f13ba7d49306537d8bd35ef3b9c010abb036cb14cd19048fb70e91913a2eac60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2202.09641",
    "kind": "arxiv",
    "version": 2
  }
}