Pith Number

pith:YY5P4EDC

pith:2003:YY5P4EDCKECLHOIKIGRJK3J6TA

not attested not anchored not stored refs pending

On the exact gravitational lens equation in spherically symmetric and static spacetimes

Volker Perlick

arxiv:gr-qc/0307072 v2 · 2003-07-15 · 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{YY5P4EDCKECLHOIKIGRJK3J6TA}

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

3 papers in Pith

Observational signatures of negative mass wormholes through their shadows

Gravitational lensing time delay beyond the Shapiro/geometry split

Relative Magnification Factor of Point Sources on Accretion Disks

Receipt and verification

First computed	2026-07-04T17:22:17.196132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c63afe10625104b3b90a41a2956d3e982128c70e7dda64bcb0a471557f939577

Aliases

arxiv: gr-qc/0307072 · arxiv_version: gr-qc/0307072v2 · doi: 10.48550/arxiv.gr-qc/0307072 · pith_short_12: YY5P4EDCKECL · pith_short_16: YY5P4EDCKECLHOIK · pith_short_8: YY5P4EDC

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/YY5P4EDCKECLHOIKIGRJK3J6TA \
  | 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: c63afe10625104b3b90a41a2956d3e982128c70e7dda64bcb0a471557f939577

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b48b28989f569e06b92dc88b3fcdfadaa55e12b1fa05be34f1c956f844f8d79",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2003-07-15T22:07:38Z",
    "title_canon_sha256": "972ead1ac74e74ac553bcb13166adb5f69819af81509e9d82cf872ca3e2a5fd7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0307072",
    "kind": "arxiv",
    "version": 2
  }
}