Pith Number

pith:PYGPBU2V

pith:2016:PYGPBU2VLTEU5QXSIBEP444GJ3

not attested not anchored not stored refs pending

Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem

Asahi Ishihara, Hideki Asada, Takao Kitamura, Toshiaki Ono, Yusuke Suzuki

arxiv:1604.08308 v2 · 2016-04-28 · gr-qc · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PYGPBU2VLTEU5QXSIBEP444GJ3}

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

5 papers in Pith

Boundary-only weak deflection angles from isothermal optical geometry

Quasinormal Modes and Neutrino Energy Deposition for a Magnetically Charged Black Hole in a Hernquist Dark Matter Halo

Shadow dependent phenomenology framework for rotating black hole metric

Light Deflection and Greybody Bound Around a BTZ-ModMax Black Hole in Plasma Medium

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

Receipt and verification

First computed	2026-05-18T01:01:57.771825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e0cf0d3555cc94ec2f24048fe73864efae60dc05f30e23f7c9fda16bcbfcd08

Aliases

arxiv: 1604.08308 · arxiv_version: 1604.08308v2 · doi: 10.48550/arxiv.1604.08308 · pith_short_12: PYGPBU2VLTEU · pith_short_16: PYGPBU2VLTEU5QXS · pith_short_8: PYGPBU2V

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/PYGPBU2VLTEU5QXSIBEP444GJ3 \
  | 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: 7e0cf0d3555cc94ec2f24048fe73864efae60dc05f30e23f7c9fda16bcbfcd08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2aa260d4ecc6efb914a8768688dc64e0d38aca0f989ba66b3b70fdaea8084edd",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2016-04-28T05:39:58Z",
    "title_canon_sha256": "c24a39b58e9fc1049eb45e279e6e502e93e31a4ce3dc71695ad6a987c1091435"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.08308",
    "kind": "arxiv",
    "version": 2
  }
}