Pith Number

pith:PRN44YRN

pith:2002:PRN44YRNQ3JVV7WNZMMHZDUBGK

not attested not anchored not stored refs pending

Quasi-Equatorial Gravitational Lensing by Spinning Black Holes in the Strong Field Limit

V. Bozza

arxiv:gr-qc/0210109 v2 · 2002-10-31 · gr-qc · 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{PRN44YRNQ3JVV7WNZMMHZDUBGK}

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	2026-07-04T17:22:17.182993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c5bce622d86d35afecdcb187c8e81329ae254781bd45253840bea6780999d16

Aliases

arxiv: gr-qc/0210109 · arxiv_version: gr-qc/0210109v2 · doi: 10.48550/arxiv.gr-qc/0210109 · pith_short_12: PRN44YRNQ3JV · pith_short_16: PRN44YRNQ3JVV7WN · pith_short_8: PRN44YRN

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/PRN44YRNQ3JVV7WNZMMHZDUBGK \
  | 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: 7c5bce622d86d35afecdcb187c8e81329ae254781bd45253840bea6780999d16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c2f19b979d71533c4d15a31f3a698fbf766cca56a55f2bb4b6bd0e663129ca6",
    "cross_cats_sorted": [
      "astro-ph"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2002-10-31T17:35:55Z",
    "title_canon_sha256": "7ae0d21c1e466745679511f2a8d193aebb49394ae48f38eda5b9d3ec84ab0d4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0210109",
    "kind": "arxiv",
    "version": 2
  }
}