Pith Number

pith:QW5GQ5U3

pith:2002:QW5GQ5U33BC6E6WEOIO3DXWFSN

not attested not anchored not stored refs pending

The Mean Number of Extra Micro-Image Pairs for Macro-Lensed Quasars

Joachim Wambsganss, Jonathan Granot, Paul L. Schechter

arxiv:astro-ph/0208439 v2 · 2002-08-23 · 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{QW5GQ5U33BC6E6WEOIO3DXWFSN}

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	2026-05-18T01:07:44.554269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85ba68769bd845e27ac4721db1dec5935f7110b7fef23df25a76b7336aa4b71c

Aliases

arxiv: astro-ph/0208439 · arxiv_version: astro-ph/0208439v2 · doi: 10.48550/arxiv.astro-ph/0208439 · pith_short_12: QW5GQ5U33BC6 · pith_short_16: QW5GQ5U33BC6E6WE · pith_short_8: QW5GQ5U3

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/QW5GQ5U33BC6E6WEOIO3DXWFSN \
  | 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: 85ba68769bd845e27ac4721db1dec5935f7110b7fef23df25a76b7336aa4b71c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4c36ab1548526210170ec94f35f7f4e434a2a9336c68fd5400d7b446e71b1e8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2002-08-23T19:28:42Z",
    "title_canon_sha256": "215ace8f3e44ba86cbb10dade49fd9b82d55082eb03dd5ab09b1390fa68e2555"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0208439",
    "kind": "arxiv",
    "version": 2
  }
}