Pith Number

pith:UE3WID2F

pith:2006:UE3WID2FL5DUHB3TRLCGMLIB5K

not attested not anchored not stored refs pending

Analytical Kerr black hole lensing in the weak deflection limit

2) ((1) Univ. Zurich, (2) Univ. Salerno), F. De Luca (1, M. Sereno (1)

arxiv:astro-ph/0609435 v2 · 2006-09-15 · astro-ph · gr-qc

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UE3WID2FL5DUHB3TRLCGMLIB5K}

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	2026-07-04T16:59:24.618967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a137640f455f474387738ac4662d01ea8706957526c51df51611a9199e5ff90b

Aliases

arxiv: astro-ph/0609435 · arxiv_version: astro-ph/0609435v2 · doi: 10.48550/arxiv.astro-ph/0609435 · pith_short_12: UE3WID2FL5DU · pith_short_16: UE3WID2FL5DUHB3T · pith_short_8: UE3WID2F

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/UE3WID2FL5DUHB3TRLCGMLIB5K \
  | 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: a137640f455f474387738ac4662d01ea8706957526c51df51611a9199e5ff90b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "552525c8e9d3fbbed8d4157dcb93cb1922a32fc56ee0152b7a4a208941fe9f64",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2006-09-15T12:43:18Z",
    "title_canon_sha256": "d7c999ca24daee1fedc86e4cc108977fb342a874892a4f04af36c8a5f5a0ad47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0609435",
    "kind": "arxiv",
    "version": 2
  }
}