Pith Number

pith:QKQCU76M

pith:1998:QKQCU76MW26PTYQOUMY5JHNFKG

not attested not anchored not stored refs pending

Gravitational Lensing in Astronomy

Germany), Joachim Wambsganss (Astrophysikalisches Institut Potsdam

arxiv:astro-ph/9812021 v1 · 1998-12-01 · astro-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QKQCU76MW26PTYQOUMY5JHNFKG}

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

Astrophysical environment around a black hole in the braneworld and its optical signatures

Receipt and verification

First computed	2026-05-18T01:40:13.565005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82a02a7fccb6bcf9e20ea331d49da55195b95cb5e02da52c77543d4937be2c15

Aliases

arxiv: astro-ph/9812021 · arxiv_version: astro-ph/9812021v1 · doi: 10.48550/arxiv.astro-ph/9812021 · pith_short_12: QKQCU76MW26P · pith_short_16: QKQCU76MW26PTYQO · pith_short_8: QKQCU76M

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/QKQCU76MW26PTYQOUMY5JHNFKG \
  | 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: 82a02a7fccb6bcf9e20ea331d49da55195b95cb5e02da52c77543d4937be2c15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e05fc6b7342380caef9a25cffd6b16f9ea285ef1cd21a67a621bf9955629be75",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1998-12-01T17:01:08Z",
    "title_canon_sha256": "df4417b20fd08b512de639ab716b1e8494f208cab9e766c7922305a0cf41cff4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9812021",
    "kind": "arxiv",
    "version": 1
  }
}