Pith Number

pith:UZ4W7CIA

pith:2006:UZ4W7CIAMJJUF4O5F2CAA7UPLN

not attested not anchored not stored refs pending

Smoothing Algorithms and High-order Singularities in Gravitational Lensing

Guo-Liang Li, M. Bartelmann, S. Mao, X. Kang, Y.P. Jing

arxiv:astro-ph/0603557 v2 · 2006-03-21 · 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{UZ4W7CIAMJJUF4O5F2CAA7UPLN}

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.

Receipt and verification

First computed	2026-05-18T04:29:04.904448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6796f8900625342f1dd2e84007e8f5b4b9b8e0c4b0b505fae6e856456682783

Aliases

arxiv: astro-ph/0603557 · arxiv_version: astro-ph/0603557v2 · doi: 10.48550/arxiv.astro-ph/0603557 · pith_short_12: UZ4W7CIAMJJU · pith_short_16: UZ4W7CIAMJJUF4O5 · pith_short_8: UZ4W7CIA

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/UZ4W7CIAMJJUF4O5F2CAA7UPLN \
  | 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: a6796f8900625342f1dd2e84007e8f5b4b9b8e0c4b0b505fae6e856456682783

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6366a5e50c480213f7b592a24eb13450d7a37d0c3c2bfdc580f99326e90cff88",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2006-03-21T08:21:55Z",
    "title_canon_sha256": "bc6ec44a5f484ec4a955f1fb15907e7a3417dff339118178a7e9fec73cfe0d9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0603557",
    "kind": "arxiv",
    "version": 2
  }
}