Pith Number

pith:DZL4Q2A5

pith:2000:DZL4Q2A5NK2VXLE4EWQUHFGVQM

not attested not anchored not stored refs pending

Gravitational Lenses With More Than Four Images: I. Classification of Caustics

C. R. Keeton (Arizona), H. J. Witt (AIP Potsdam), MPA Garching), S. Mao (Jodrell Bank

arxiv:astro-ph/0002401 v1 · 2000-02-22 · 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{DZL4Q2A5NK2VXLE4EWQUHFGVQM}

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

Identifying multiple images of gravitational-wave sources lensed by elliptical lensing potentials

Receipt and verification

First computed	2026-07-04T16:16:05.956908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e57c8681d6ab55bac9c25a14394d583295ff5628c276a3826423ebb49e00b46

Aliases

arxiv: astro-ph/0002401 · arxiv_version: astro-ph/0002401v1 · doi: 10.48550/arxiv.astro-ph/0002401 · pith_short_12: DZL4Q2A5NK2V · pith_short_16: DZL4Q2A5NK2VXLE4 · pith_short_8: DZL4Q2A5

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/DZL4Q2A5NK2VXLE4EWQUHFGVQM \
  | 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: 1e57c8681d6ab55bac9c25a14394d583295ff5628c276a3826423ebb49e00b46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6617a4f4b0c9bdd7a6adb03b8fd2e54e7254ac4db2d961da985cf1673017511d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2000-02-22T03:50:04Z",
    "title_canon_sha256": "274e6da28f1201c7c39af27cde22effbe04d5905f771bc5f95cb34f9a359c961"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0002401",
    "kind": "arxiv",
    "version": 1
  }
}