Pith Number

pith:32KEH6E7

pith:2022:32KEH6E7NTMC745GASTILLQBQ4

not attested not anchored not stored refs pending

Gravitational Lensing by Black Holes with Multiple Photon Spheres

Guangzhou Guo, Houwen Wu, Peng Wang, Xin Jiang

arxiv:2204.13948 v2 · 2022-04-29 · gr-qc · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{32KEH6E7NTMC745GASTILLQBQ4}

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

Optical Appearance of Scalarized Kerr-Newman Black Holes with Multiple Light Rings

Topologically equivalent yet radiatively distinct orbits in EMRI system

Receipt and verification

First computed	2026-07-05T04:39:36.421239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de9443f89f6cd82ff3a604a685ae01871630fceb003d2c057347046c1262118d

Aliases

arxiv: 2204.13948 · arxiv_version: 2204.13948v2 · doi: 10.48550/arxiv.2204.13948 · pith_short_12: 32KEH6E7NTMC · pith_short_16: 32KEH6E7NTMC745G · pith_short_8: 32KEH6E7

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/32KEH6E7NTMC745GASTILLQBQ4 \
  | 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: de9443f89f6cd82ff3a604a685ae01871630fceb003d2c057347046c1262118d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6a1af643854921b9edf355179cd39963e4bba2cd89451a8ba19f5234c10a530",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2022-04-29T08:47:56Z",
    "title_canon_sha256": "337d358d3f9485d404e338ba9aeb9f576e0f9f9b5218b8d49b31c9711ab1b607"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2204.13948",
    "kind": "arxiv",
    "version": 2
  }
}