Pith Number

pith:GZWFK3FM

pith:1998:GZWFK3FM3AEFCP25LF7EZQAKX4

not attested not anchored not stored refs pending

Role of the scalar field in gravitational lensing

(2) University of Zululand, D. Narasimha (1), India, K. S. Virbhadra (1-2), S. Africa), S. M. Chitre (1) ((1) Tata Institute of Fundamental Research

arxiv:astro-ph/9801174 v2 · 1998-01-18 · astro-ph · gr-qc · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GZWFK3FM3AEFCP25LF7EZQAKX4}

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

Unveiling horizons in quantum critical collapse

Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes

Receipt and verification

First computed	2026-05-18T04:21:40.282595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

366c556cacd808513f5d597e4cc00abf044ec62ce644c1f1a36cb6510e4dd0ab

Aliases

arxiv: astro-ph/9801174 · arxiv_version: astro-ph/9801174v2 · doi: 10.48550/arxiv.astro-ph/9801174 · pith_short_12: GZWFK3FM3AEF · pith_short_16: GZWFK3FM3AEFCP25 · pith_short_8: GZWFK3FM

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/GZWFK3FM3AEFCP25LF7EZQAKX4 \
  | 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: 366c556cacd808513f5d597e4cc00abf044ec62ce644c1f1a36cb6510e4dd0ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b427cbcc03f2dd2d73f3b0f25009c31348fbbbc02da3b008ca4bdf1bc9f93ab0",
    "cross_cats_sorted": [
      "gr-qc",
      "hep-th"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1998-01-18T13:10:30Z",
    "title_canon_sha256": "223dfb2faaf76d49acbf1295815fd170d5d20724c08e8e13ce9d0ab01f1ea8d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9801174",
    "kind": "arxiv",
    "version": 2
  }
}