Pith Number

pith:7HQLZ4CU

pith:1997:7HQLZ4CUPUTWJUZA6HZKTMCLVT

not attested not anchored not stored refs pending

Gravitational Lensing of Quasars by Spiral Galaxies

Abraham Loeb (Harvard Univ)

arxiv:astro-ph/9701100 v1 · 1997-01-15 · 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{7HQLZ4CUPUTWJUZA6HZKTMCLVT}

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	2026-05-18T01:07:40.284727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9e0bcf0547d2764d320f1f2a9b04baccc2b7ba66c3fe9d4a7bc57292dbada53

Aliases

arxiv: astro-ph/9701100 · arxiv_version: astro-ph/9701100v1 · doi: 10.48550/arxiv.astro-ph/9701100 · pith_short_12: 7HQLZ4CUPUTW · pith_short_16: 7HQLZ4CUPUTWJUZA · pith_short_8: 7HQLZ4CU

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/7HQLZ4CUPUTWJUZA6HZKTMCLVT \
  | 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: f9e0bcf0547d2764d320f1f2a9b04baccc2b7ba66c3fe9d4a7bc57292dbada53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5ed2154ec3eac0a6d13fe50d267dcfb9ee78de309fcd70af23596be0a46d499",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1997-01-15T22:15:09Z",
    "title_canon_sha256": "e21262346f42d759fbdbf7ca03a9c3ac463d85b9cc9670926e8412eafdbbe226"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9701100",
    "kind": "arxiv",
    "version": 1
  }
}