Pith Number

pith:QBKRCF3I

pith:2006:QBKRCF3IBLUTORD2W7EOVUGUW4

not attested not anchored not stored refs pending

Effects of early dark energy on strong cluster lensing

C. Fedeli, M. Bartelmann

arxiv:astro-ph/0607069 v2 · 2006-07-05 · 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{QBKRCF3IBLUTORD2W7EOVUGUW4}

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	2026-07-04T15:31:23.308677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80551117680ae937447ab7c8ead0d4b721ea86e54ee95c5d24228d4da63205f8

Aliases

arxiv: astro-ph/0607069 · arxiv_version: astro-ph/0607069v2 · doi: 10.48550/arxiv.astro-ph/0607069 · pith_short_12: QBKRCF3IBLUT · pith_short_16: QBKRCF3IBLUTORD2 · pith_short_8: QBKRCF3I

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/QBKRCF3IBLUTORD2W7EOVUGUW4 \
  | 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: 80551117680ae937447ab7c8ead0d4b721ea86e54ee95c5d24228d4da63205f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45fd579dca51f9281c3ae01762e24b1e9dd9cb823cadb42b395e20c7baac97b5",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2006-07-05T13:36:20Z",
    "title_canon_sha256": "df06ed75264596e5d8f7be5ea8167b90eefc4cd28dc2c430d59716bf3d343c6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0607069",
    "kind": "arxiv",
    "version": 2
  }
}