Pith Number

pith:ZMP7ITOX

pith:2001:ZMP7ITOXH3YO34AQ45ZUMX4MY4

not attested not anchored not stored refs pending

Computational Methods for Gravitational Lensing

Charles R. Keeton

arxiv:astro-ph/0102340 v1 · 2001-02-20 · 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{ZMP7ITOXH3YO34AQ45ZUMX4MY4}

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

Determining the spatial origin of X-ray and optical emission in the $z = 3.1$ strongly lensed radio-quiet quasar GraL J065904.1+162909 to hundreds of parsecs

Receipt and verification

First computed	2026-07-04T14:11:04.604098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb1ff44dd73ef0edf010e773465f8cc70bf4fa13975ad8d049476e389659c8ba

Aliases

arxiv: astro-ph/0102340 · arxiv_version: astro-ph/0102340v1 · doi: 10.48550/arxiv.astro-ph/0102340 · pith_short_12: ZMP7ITOXH3YO · pith_short_16: ZMP7ITOXH3YO34AQ · pith_short_8: ZMP7ITOX

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/ZMP7ITOXH3YO34AQ45ZUMX4MY4 \
  | 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: cb1ff44dd73ef0edf010e773465f8cc70bf4fa13975ad8d049476e389659c8ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74020b05231eb661abed2ef72d606fab90b01d2ed46c6fe0aac3020f2ea3fd00",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2001-02-20T18:22:36Z",
    "title_canon_sha256": "6d0c1725434d41e3608f36da95cfb345447306f044f669a821530536f5e94cbf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0102340",
    "kind": "arxiv",
    "version": 1
  }
}