Pith Number

pith:GSPPDF3A

pith:2004:GSPPDF3AM7LC7FIC2WE64J3KVJ

not attested not anchored not stored refs pending

Simulations of Strong Gravitational Lensing with Substructure

(2) UC Santa Cruz), Adam Amara (1), Jeremiah P. Ostriker (1) ((1) IoA Cambridge, R. Benton Metcalf (2), Thomas J. Cox (2)

arxiv:astro-ph/0411587 v2 · 2004-11-19 · 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{GSPPDF3AM7LC7FIC2WE64J3KVJ}

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 metric solution for rotating black holes embedded in dark matter halos with central spikes

Receipt and verification

First computed	2026-07-04T16:45:16.344703Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

349ef1976067d62f9502d589ee276aaa5625cc1f0e327d5d35300134836cb2fe

Aliases

arxiv: astro-ph/0411587 · arxiv_version: astro-ph/0411587v2 · doi: 10.48550/arxiv.astro-ph/0411587 · pith_short_12: GSPPDF3AM7LC · pith_short_16: GSPPDF3AM7LC7FIC · pith_short_8: GSPPDF3A

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/GSPPDF3AM7LC7FIC2WE64J3KVJ \
  | 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: 349ef1976067d62f9502d589ee276aaa5625cc1f0e327d5d35300134836cb2fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05a415a687a720132e0926ebf2d2ba8829781bbba0ffb437b4a8616a8bb415aa",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2004-11-19T23:18:25Z",
    "title_canon_sha256": "3578b58f0d9eec58b93402fdb043e4c527aeb82bcfee757a1a59243b5621d92a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0411587",
    "kind": "arxiv",
    "version": 2
  }
}