Pith Number

pith:PW4SPBK3

pith:2013:PW4SPBK3UH763XBPOJA3HAQWEA

not attested not anchored not stored refs pending

Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens

G. L. Li, W. P. Lin, X. Kang, Z. Chu

arxiv:1302.5482 v1 · 2013-02-22 · 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{PW4SPBK3UH763XBPOJA3HAQWEA}

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.

Receipt and verification

First computed	2026-05-18T03:32:07.294200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7db927855ba1ffeddc2f7241b38216203bba24e90f869baac33a0ca8e09c589f

Aliases

arxiv: 1302.5482 · arxiv_version: 1302.5482v1 · doi: 10.48550/arxiv.1302.5482 · pith_short_12: PW4SPBK3UH76 · pith_short_16: PW4SPBK3UH763XBP · pith_short_8: PW4SPBK3

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/PW4SPBK3UH763XBPOJA3HAQWEA \
  | 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: 7db927855ba1ffeddc2f7241b38216203bba24e90f869baac33a0ca8e09c589f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cee0e016866388290b2dbb4ee59fb9392afb8df7133818b2e01be76ef9a476e6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2013-02-22T04:48:38Z",
    "title_canon_sha256": "383079e3cd9eea64a3be9d63af5d86b3d94f695fac238f6825c8ab8c6c234a75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.5482",
    "kind": "arxiv",
    "version": 1
  }
}