Pith Number

pith:JKB6XUS5

pith:2022:JKB6XUS5Z34NWDCYNZMCSHXQ3E

not attested not anchored not stored refs pending

Black Holes with Multiple Photon Spheres

Guangzhou Guo, Haitang Yang, Houwen Wu, Peng Wang, Yuhang Lu

arxiv:2212.12901 v3 · 2022-12-25 · 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{JKB6XUS5Z34NWDCYNZMCSHXQ3E}

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

Topological charge and black hole photon spheres in massive gravity

Energy conditions in static, spherically symmetric spacetimes and effective geometries

Receipt and verification

First computed	2026-07-05T06:25:17.935821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a83ebd25dcef8db0c586e58291ef0d93dadfe2ca8f91660c105dda59cf2c371

Aliases

arxiv: 2212.12901 · arxiv_version: 2212.12901v3 · doi: 10.48550/arxiv.2212.12901 · pith_short_12: JKB6XUS5Z34N · pith_short_16: JKB6XUS5Z34NWDCY · pith_short_8: JKB6XUS5

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/JKB6XUS5Z34NWDCYNZMCSHXQ3E \
  | 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: 4a83ebd25dcef8db0c586e58291ef0d93dadfe2ca8f91660c105dda59cf2c371

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c45a9beabe8974e500ccda06d79a6b22a2e03ff0f1689d2808235f04644d75ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2022-12-25T13:35:03Z",
    "title_canon_sha256": "8fc5ac7bedb3df30256a21926b6b2c2311d6e06256743e67537f411f251f75d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.12901",
    "kind": "arxiv",
    "version": 3
  }
}