Pith Number

pith:3PVCWEJO

pith:2012:3PVCWEJOZQL3MEIUKANV2RINHH

not attested not anchored not stored refs pending

Gravitational lens equation. Critical solutions and magnification near folds and cusps

(2) National University of Kyiv-Mohyla Academy, A. N. Alexandrov (1), Kiev, S. M. Koval (2), Taras Shevchenko National University of Kyiv, Ukraine, Ukraine), V. I. Zhdanov (1) ((1) Astronomical Observatory

arxiv:1212.6565 v1 · 2012-12-28 · astro-ph.CO · astro-ph.GA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3PVCWEJOZQL3MEIUKANV2RINHH}

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	2026-05-18T03:37:31.546022Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbea2b112ecc17b61114501b5d450d39f29a1e63e1736f97d6374a48075b90df

Aliases

arxiv: 1212.6565 · arxiv_version: 1212.6565v1 · doi: 10.48550/arxiv.1212.6565 · pith_short_12: 3PVCWEJOZQL3 · pith_short_16: 3PVCWEJOZQL3MEIU · pith_short_8: 3PVCWEJO

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/3PVCWEJOZQL3MEIUKANV2RINHH \
  | 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: dbea2b112ecc17b61114501b5d450d39f29a1e63e1736f97d6374a48075b90df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8681aba77e791024f50b19ab05f009eaa28c869d1aa939f825066bbad6d2cbb",
    "cross_cats_sorted": [
      "astro-ph.GA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2012-12-28T21:12:47Z",
    "title_canon_sha256": "3dc1955ab19823a90ccfc6d7b715a3572c1e2aaa027058f6a8886a0fb8633a4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6565",
    "kind": "arxiv",
    "version": 1
  }
}