Pith Number

pith:YZIQTAY7

pith:2024:YZIQTAY7G642M7AVOQCU6S2477

not attested not anchored not stored refs pending

Gravitational Lensing Using Werner's Method in Cartesian-like Coordinates

Zonghai Li

arxiv:2404.19658 v2 · 2024-04-30 · 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{YZIQTAY7G642M7AVOQCU6S2477}

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

Boundary-only weak deflection angles from isothermal optical geometry

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

Receipt and verification

First computed	2026-07-05T10:32:26.476528Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c65109831f37b9a67c1574054f4b5cffc1b2ef34791128ea4c7020424d6428da

Aliases

arxiv: 2404.19658 · arxiv_version: 2404.19658v2 · doi: 10.48550/arxiv.2404.19658 · pith_short_12: YZIQTAY7G642 · pith_short_16: YZIQTAY7G642M7AV · pith_short_8: YZIQTAY7

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/YZIQTAY7G642M7AVOQCU6S2477 \
  | 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: c65109831f37b9a67c1574054f4b5cffc1b2ef34791128ea4c7020424d6428da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2179e61030c87227c2ea5a00ebf21d5785e983434ecc5753b33e17b1066a17f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2024-04-30T15:55:23Z",
    "title_canon_sha256": "ad8fbe8a2d5b12958b02301b4df2c943606a3d8b61cf473ce2136e56ddd80a54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.19658",
    "kind": "arxiv",
    "version": 2
  }
}