Pith Number

pith:4WADZPE6

pith:2021:4WADZPE6T43D7LKQQ3JWGNZFPE

not attested not anchored not stored refs pending

Shadows and lensing of black holes immersed in strong magnetic fields

Carlos A. R. Herdeiro, Haroldo C. D. Lima Junior, Lu\'is C. B. Crispino, Pedro V. P. Cunha

arxiv:2104.09577 v2 · 2021-04-19 · gr-qc · astro-ph.HE · 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{4WADZPE6T43D7LKQQ3JWGNZFPE}

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

Topological charge and black hole photon spheres in massive gravity

Receipt and verification

First computed	2026-07-05T03:05:49.516412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5803cbc9e9f363fad5086d363372579357d05b10fff5c3a2c9b368309551538

Aliases

arxiv: 2104.09577 · arxiv_version: 2104.09577v2 · doi: 10.48550/arxiv.2104.09577 · pith_short_12: 4WADZPE6T43D · pith_short_16: 4WADZPE6T43D7LKQ · pith_short_8: 4WADZPE6

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/4WADZPE6T43D7LKQQ3JWGNZFPE \
  | 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: e5803cbc9e9f363fad5086d363372579357d05b10fff5c3a2c9b368309551538

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c34949e284f1e406d824b277054bf1646e91604c7765c9f857f1ea58e953d902",
    "cross_cats_sorted": [
      "astro-ph.HE",
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-04-19T19:15:55Z",
    "title_canon_sha256": "00999c04664055316015737c1a04a8f049c01fd72328b4a2cd2209e37073c007"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.09577",
    "kind": "arxiv",
    "version": 2
  }
}