Pith Number

pith:QY4ZCAEO

pith:2022:QY4ZCAEO3BSZSD5MTDK77IA6D6

not attested not anchored not stored refs pending

Gravitational Lensing of Schwarzschild and Charged Black Holes Immersed in Perfect Fluid Dark Matter Halo

Chen-Kai Qiao, Mi Zhou

arxiv:2212.13311 v3 · 2022-12-26 · gr-qc · astro-ph.GA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QY4ZCAEO3BSZSD5MTDK77IA6D6}

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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

Periodic orbits and gravitational waveforms around a Schwarzschild black hole with a cloud of strings embedded in perfect fluid dark matter

Receipt and verification

First computed	2026-07-05T07:53:58.898132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

863991008ed865990fac98d5ffa01e1f91acd2fe0d40bc8035c9c47e45c6c9a4

Aliases

arxiv: 2212.13311 · arxiv_version: 2212.13311v3 · doi: 10.48550/arxiv.2212.13311 · pith_short_12: QY4ZCAEO3BSZ · pith_short_16: QY4ZCAEO3BSZSD5M · pith_short_8: QY4ZCAEO

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/QY4ZCAEO3BSZSD5MTDK77IA6D6 \
  | 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: 863991008ed865990fac98d5ffa01e1f91acd2fe0d40bc8035c9c47e45c6c9a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dac2854ee8b3de9dc5b898729e0cf2e417cef836d1a534961bb8a196e8316543",
    "cross_cats_sorted": [
      "astro-ph.GA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2022-12-26T22:26:38Z",
    "title_canon_sha256": "94eb7221840f758a345f097a22e6c45289bc5fdbd4f9d52eba4f011c6d49b61b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.13311",
    "kind": "arxiv",
    "version": 3
  }
}