Pith Number

pith:7JF2XASH

pith:2019:7JF2XASHTPE2OCHOQP5KWHUGQ4

not attested not anchored not stored refs pending

Bounds on Photon Spheres and Shadows of Charged Black Holes in Einstein-Gauss-Bonnet-Maxwell Gravity

H. Lu, Liang Ma

arxiv:1912.05569 v1 · 2019-12-11 · 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{7JF2XASHTPE2OCHOQP5KWHUGQ4}

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

Photon rings and shadows of black holes with non-minimal couplings between curvature and electromagnetic field

Receipt and verification

First computed	2026-07-05T01:08:50.780920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa4bab82479bc9a708ee83faab1e86871ddaf48d32894455ded0e2d1ab65bd0e

Aliases

arxiv: 1912.05569 · arxiv_version: 1912.05569v1 · doi: 10.48550/arxiv.1912.05569 · pith_short_12: 7JF2XASHTPE2 · pith_short_16: 7JF2XASHTPE2OCHO · pith_short_8: 7JF2XASH

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/7JF2XASHTPE2OCHOQP5KWHUGQ4 \
  | 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: fa4bab82479bc9a708ee83faab1e86871ddaf48d32894455ded0e2d1ab65bd0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0f3e11ec75e6cdba1f5749997a0fcaa9fc4a50ec540f6aa1b0f6a6cc9bf831d",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2019-12-11T19:00:44Z",
    "title_canon_sha256": "7bb83f012eb8f69552f14933e7070bd70e51cf446ae7207047c05e5feeaea91d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.05569",
    "kind": "arxiv",
    "version": 1
  }
}