Pith Number

pith:IEPN7CHZ

pith:2022:IEPN7CHZUMBGQMHNZQYVLHQAF6

not attested not anchored not stored refs pending

Shadows and Strong Gravitational Lensing by Van der Waals Black Hole in Homogeneous Plasma

Niyaz Uddin Molla, Ujjal Debnath

arxiv:2212.02104 v1 · 2022-12-05 · gr-qc · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IEPN7CHZUMBGQMHNZQYVLHQAF6}

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

A note on methods for computing the critical curve of Kerr-like black holes

Receipt and verification

First computed	2026-07-05T05:22:20.515560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

411edf88f9a3026830edcc31559e002fbd0ef6c20c4f0445dce4c955fa316664

Aliases

arxiv: 2212.02104 · arxiv_version: 2212.02104v1 · doi: 10.48550/arxiv.2212.02104 · pith_short_12: IEPN7CHZUMBG · pith_short_16: IEPN7CHZUMBGQMHN · pith_short_8: IEPN7CHZ

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/IEPN7CHZUMBGQMHNZQYVLHQAF6 \
  | 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: 411edf88f9a3026830edcc31559e002fbd0ef6c20c4f0445dce4c955fa316664

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e577f2e9fa1478f28d973fcb50109acfb72757f4eb876855687bd6d7f6dd6f6",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2022-12-05T08:58:12Z",
    "title_canon_sha256": "1b5b6a60c2bdbe1b537704f26d14e06054ee90170f6a03f422e7adfc72724025"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.02104",
    "kind": "arxiv",
    "version": 1
  }
}