Pith Number

pith:L5FNNUW6

pith:2012:L5FNNUW65PY2N5FRJHXKMGMI2F

not attested not anchored not stored refs pending

Strong gravitational lensing by Schwarzschild black hole

Tushar Kanti Dey

arxiv:1208.3306 v1 · 2012-08-16 · 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{L5FNNUW65PY2N5FRJHXKMGMI2F}

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	2026-05-18T03:48:36.221958Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f4ad6d2deebf1a6f4b149eea61988d143e09356bd64cdd9b6660fc4d4f701c0

Aliases

arxiv: 1208.3306 · arxiv_version: 1208.3306v1 · doi: 10.48550/arxiv.1208.3306 · pith_short_12: L5FNNUW65PY2 · pith_short_16: L5FNNUW65PY2N5FR · pith_short_8: L5FNNUW6

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/L5FNNUW65PY2N5FRJHXKMGMI2F \
  | 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: 5f4ad6d2deebf1a6f4b149eea61988d143e09356bd64cdd9b6660fc4d4f701c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "993f259bfbd44eca0be9d2bc0239661f3e644aa6bfb31f86ba1e420aad8bc80b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-08-16T07:37:44Z",
    "title_canon_sha256": "4a4d2a38b25dbeafd0fd554bb5a823a9d259a4ace5f90ac5fe25a29aebc26e4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3306",
    "kind": "arxiv",
    "version": 1
  }
}