Pith Number

pith:5WIJBDJ4

pith:1994:5WIJBDJ4QP6JFWACIQF35TJLIC

not attested not anchored not stored refs pending

Light Propagation in Arbitrary Spacetimes and the Gravitational Lens Approximation

Juergen Ehlers, Peter Schneider, Stella Seitz

arxiv:astro-ph/9403056 v1 · 1994-03-24 · 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{5WIJBDJ4QP6JFWACIQF35TJLIC}

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

2 papers in Pith

Covariant variation for point-particle Lagrangians

Gravitational lensing time delay beyond the Shapiro/geometry split

Receipt and verification

First computed	2026-07-04T17:25:34.168177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed90908d3c83fc92d802440bbecd2b40aec2484ea8f0ec20d723d421dea04964

Aliases

arxiv: astro-ph/9403056 · arxiv_version: astro-ph/9403056v1 · doi: 10.48550/arxiv.astro-ph/9403056 · pith_short_12: 5WIJBDJ4QP6J · pith_short_16: 5WIJBDJ4QP6JFWAC · pith_short_8: 5WIJBDJ4

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/5WIJBDJ4QP6JFWACIQF35TJLIC \
  | 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: ed90908d3c83fc92d802440bbecd2b40aec2484ea8f0ec20d723d421dea04964

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23713992cfdb593296b681244cd1712bdbeec63d4d889fdc96d4cacebc8aba21",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1994-03-24T14:15:17Z",
    "title_canon_sha256": "6a1d3df2f11f619a30d028233a887cd51ec23aebf8b1665297f41e6ec3cf1f9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9403056",
    "kind": "arxiv",
    "version": 1
  }
}