Pith Number

pith:JUEAQQ5K

pith:2007:JUEAQQ5KWSDP6NPLJ5EUYDNHJO

not attested not anchored not stored refs pending

Strong lensing optical depths in a \LambdaCDM universe

Jan Hartlap, Peter Schneider, Simon D.M. White, Stefan Hilbert

arxiv:astro-ph/0703803 v2 · 2007-03-30 · 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{JUEAQQ5KWSDP6NPLJ5EUYDNHJO}

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	2026-07-04T15:05:58.757495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d080843aab486ff35eb4f494c0da74ba441824d00ba434d1746fe15283ae1d6

Aliases

arxiv: astro-ph/0703803 · arxiv_version: astro-ph/0703803v2 · doi: 10.48550/arxiv.astro-ph/0703803 · pith_short_12: JUEAQQ5KWSDP · pith_short_16: JUEAQQ5KWSDP6NPL · pith_short_8: JUEAQQ5K

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/JUEAQQ5KWSDP6NPLJ5EUYDNHJO \
  | 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: 4d080843aab486ff35eb4f494c0da74ba441824d00ba434d1746fe15283ae1d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e22f19a04956b72cf444d5aa1c9b16d625816e7806975856cd8640346200474d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2007-03-30T16:24:52Z",
    "title_canon_sha256": "71899be7ca454e912894b4fa50b5c14d3e55f62108ffee264dbffb67c55f3924"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0703803",
    "kind": "arxiv",
    "version": 2
  }
}