Pith Number

pith:PW2SODYX

pith:2012:PW2SODYXGTIOKMZN56TZAZ37DI

not attested not anchored not stored refs pending

Gravitational lensing in the Kerr-Randers optical geometry

M. C. Werner

arxiv:1205.3876 v2 · 2012-05-17 · gr-qc · astro-ph.GA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PW2SODYXGTIOKMZN56TZAZ37DI}

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.

Cited by

4 papers in Pith

Massive particle surfaces and black hole shadows from intrinsic curvature

Boundary-only weak deflection angles from isothermal optical geometry

Hadronic lensing

Receipt and verification

First computed	2026-05-18T01:57:26.152942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7db5270f1734d0e5332defa790677f1a2fbb124e4eea436191da8add44a4b16b

Aliases

arxiv: 1205.3876 · arxiv_version: 1205.3876v2 · doi: 10.48550/arxiv.1205.3876 · pith_short_12: PW2SODYXGTIO · pith_short_16: PW2SODYXGTIOKMZN · pith_short_8: PW2SODYX

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/PW2SODYXGTIOKMZN56TZAZ37DI \
  | 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: 7db5270f1734d0e5332defa790677f1a2fbb124e4eea436191da8add44a4b16b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "760b3f3b060167c02c131caa9d310d72d87882e7f4a373fa6c543e76ea5618b5",
    "cross_cats_sorted": [
      "astro-ph.GA",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-05-17T08:10:36Z",
    "title_canon_sha256": "4a757283e9f4a0ccad4c37a16c617a34f5c23c2c399de0972500c96832c18d33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.3876",
    "kind": "arxiv",
    "version": 2
  }
}