Pith Number

pith:HXHPDWG6

pith:2000:HXHPDWG6M6FBSABZ4RGJZHO2E5

not attested not anchored not stored refs pending

What Fraction of Gravitational Lens Galaxies Lie in Groups?

A. I. Zabludoff (Arizona), C. R. Keeton, D. Christlein

arxiv:astro-ph/0007288 v1 · 2000-07-19 · 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{HXHPDWG6M6FBSABZ4RGJZHO2E5}

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	2026-07-04T16:16:55.780599Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3dcef1d8de678a190039e44c9c9dda27546e1a4ef2065a8a3d1a60e3ae46f003

Aliases

arxiv: astro-ph/0007288 · arxiv_version: astro-ph/0007288v1 · doi: 10.48550/arxiv.astro-ph/0007288 · pith_short_12: HXHPDWG6M6FB · pith_short_16: HXHPDWG6M6FBSABZ · pith_short_8: HXHPDWG6

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/HXHPDWG6M6FBSABZ4RGJZHO2E5 \
  | 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: 3dcef1d8de678a190039e44c9c9dda27546e1a4ef2065a8a3d1a60e3ae46f003

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84eec5b1e3796de579988e8e23ccb3fb4f573e378c0d0a7b9ec1f405a337d76b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2000-07-19T16:18:04Z",
    "title_canon_sha256": "80e10567268c5002c9cd507a0decbcf33d6056464e00773ce7ead319e4176423"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0007288",
    "kind": "arxiv",
    "version": 1
  }
}