Pith Number

pith:QVZ4ATLV

pith:2007:QVZ4ATLVRIZYRXJWOAQFFCJ4JK

not attested not anchored not stored refs pending

Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities

C. R. Keeton, K. S. Virbhadra

arxiv:0710.2333 v1 · 2007-10-11 · gr-qc · astro-ph · hep-th · physics.class-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{QVZ4ATLVRIZYRXJWOAQFFCJ4JK}

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

5 papers in Pith

Regular black hole solutions and the quark chemical potential at the QCD phase transition

Unveiling horizons in quantum critical collapse

Boundary-only weak deflection angles from isothermal optical geometry

Weyl-type solutions with multipolar scalar fields

Receipt and verification

First computed	2026-07-04T15:27:51.876393Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8573c04d758a3388dd36702052893c4a9ec10b7a5f40a0ac5fed50b19b5fff35

Aliases

arxiv: 0710.2333 · arxiv_version: 0710.2333v1 · doi: 10.48550/arxiv.0710.2333 · pith_short_12: QVZ4ATLVRIZY · pith_short_16: QVZ4ATLVRIZYRXJW · pith_short_8: QVZ4ATLV

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/QVZ4ATLVRIZYRXJWOAQFFCJ4JK \
  | 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: 8573c04d758a3388dd36702052893c4a9ec10b7a5f40a0ac5fed50b19b5fff35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbc732cfe0b2ce93ed2856ac9147fc00bcee3c7edfa4d65828a58055f6daee8d",
    "cross_cats_sorted": [
      "astro-ph",
      "hep-th",
      "physics.class-ph"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2007-10-11T19:28:32Z",
    "title_canon_sha256": "bc75aaa64f8eed4b391db175ba982c60cb3256a452016a48455779affde97757"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.2333",
    "kind": "arxiv",
    "version": 1
  }
}