Pith Number

pith:63MS3JY6

pith:2019:63MS3JY6D4JVRU7VLD2EYH3QZG

not attested not anchored not stored refs pending

Weak gravitational lensing by two-power-law densities using the Gauss-Bonnet theorem

Ian Vega, Karlo de Leon

arxiv:1903.06951 v1 · 2019-03-16 · 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{63MS3JY6D4JVRU7VLD2EYH3QZG}

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

1 paper in Pith

Analyzing Deflection Angles and Photon Sphere Dynamics of Magnetically Charged Black Holes in Nonlinear Electrodynamic

Receipt and verification

First computed	2026-05-17T23:43:02.927583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6d92da71e1f1358d3f558f44c1f70c9934b17be67a80600dd5be97290aae8f5

Aliases

arxiv: 1903.06951 · arxiv_version: 1903.06951v1 · doi: 10.48550/arxiv.1903.06951 · pith_short_12: 63MS3JY6D4JV · pith_short_16: 63MS3JY6D4JVRU7V · pith_short_8: 63MS3JY6

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/63MS3JY6D4JVRU7VLD2EYH3QZG \
  | 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: f6d92da71e1f1358d3f558f44c1f70c9934b17be67a80600dd5be97290aae8f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b3c270fd01ae5716159cd0d14d06539aab8495d681ea3b5411851ca05614dd8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2019-03-16T16:07:18Z",
    "title_canon_sha256": "dc4bf3cd89d86c94c886c3c6dab22ef43d197f7001a6194ce6a61bcd53334be5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.06951",
    "kind": "arxiv",
    "version": 1
  }
}