Pith Number

pith:4HO75QXR

pith:2004:4HO75QXRNAL4RCR6XKR4JR576S

not attested not anchored not stored refs pending

Quasi-geometrical Optics Approximation in Gravitational Lensing

Ryuichi Takahashi

arxiv:astro-ph/0402165 v2 · 2004-02-07 · 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{4HO75QXRNAL4RCR6XKR4JR576S}

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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

Wave-optics gravitational wave lensing in modified gravity

Parameter inference of millilensed gravitational waves using neural spline flows

Receipt and verification

First computed	2026-07-04T16:42:59.444383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1ddfec2f16817c88a3ebaa3c4c7bff4bd628bcfd0f7d9eb9a19ea7305267f64

Aliases

arxiv: astro-ph/0402165 · arxiv_version: astro-ph/0402165v2 · doi: 10.48550/arxiv.astro-ph/0402165 · pith_short_12: 4HO75QXRNAL4 · pith_short_16: 4HO75QXRNAL4RCR6 · pith_short_8: 4HO75QXR

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/4HO75QXRNAL4RCR6XKR4JR576S \
  | 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: e1ddfec2f16817c88a3ebaa3c4c7bff4bd628bcfd0f7d9eb9a19ea7305267f64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53bf87e9f924ddefb901d197f084d5ca2d97e23b55ea4bdb515d365a0d4ff5a2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2004-02-07T07:47:40Z",
    "title_canon_sha256": "07e7ad65cd4e1051ad27648c57f3067b1326428718f26db44836df1643358f57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0402165",
    "kind": "arxiv",
    "version": 2
  }
}