Pith Number

pith:VZFFB5ML

pith:2003:VZFFB5MLFVP7AA24YY3LZO62D4

not attested not anchored not stored refs pending

Gravitational lensing in metric theories of gravity

M. Sereno

arxiv:astro-ph/0301290 v1 · 2003-01-15 · 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{VZFFB5MLFVP7AA24YY3LZO62D4}

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

1 paper in Pith

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes

Receipt and verification

First computed	2026-07-04T16:35:51.881349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae4a50f58b2d5ff0035cc636bcbbda1f35aeb74d77763901ddf4c35d2e8826aa

Aliases

arxiv: astro-ph/0301290 · arxiv_version: astro-ph/0301290v1 · doi: 10.48550/arxiv.astro-ph/0301290 · pith_short_12: VZFFB5MLFVP7 · pith_short_16: VZFFB5MLFVP7AA24 · pith_short_8: VZFFB5ML

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/VZFFB5MLFVP7AA24YY3LZO62D4 \
  | 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: ae4a50f58b2d5ff0035cc636bcbbda1f35aeb74d77763901ddf4c35d2e8826aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9d1113b6f5568ee98d17738495ca1e691c2e5fced46e51c5d4d9c5df74314d0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2003-01-15T13:04:20Z",
    "title_canon_sha256": "8918dcce8c8f94d70121d26f1b569e44efca7d24407674ba40c54a4869ab1700"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0301290",
    "kind": "arxiv",
    "version": 1
  }
}