Pith Number

pith:WJ4DALWI

pith:1992:WJ4DALWIQ6BHZXMUCS3IMUESPU

not attested not anchored not stored refs pending

Nonstationary Gravitational Lenses and the Fermat Principle

Valerio Faraoni

arxiv:astro-ph/9205001 v1 · 1992-05-01 · 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{WJ4DALWIQ6BHZXMUCS3IMUESPU}

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.

Receipt and verification

First computed	2026-05-18T04:17:25.634477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b278302ec887827cdd9414b68650927d240721b7350c9a00ef05545a7fa324dd

Aliases

arxiv: astro-ph/9205001 · arxiv_version: astro-ph/9205001v1 · doi: 10.48550/arxiv.astro-ph/9205001 · pith_short_12: WJ4DALWIQ6BH · pith_short_16: WJ4DALWIQ6BHZXMU · pith_short_8: WJ4DALWI

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/WJ4DALWIQ6BHZXMUCS3IMUESPU \
  | 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: b278302ec887827cdd9414b68650927d240721b7350c9a00ef05545a7fa324dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "992cb1af69e1b853fdf760382b50d648d91f1f3bf2b1bfb77791ffe122fbe11f",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1992-05-01T16:41:45Z",
    "title_canon_sha256": "32d4d0a1d4c359fc41ec0fbccf5e1750cf8e929df930043aa94ccb43c99aeb22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9205001",
    "kind": "arxiv",
    "version": 1
  }
}