Pith Number

pith:D2DIKFND

pith:2016:D2DIKFNDB42BDDAXHP6E6IJ2VP

not attested not anchored not stored refs pending

Magnification relations of quad lenses and applications on Einstein crosses

G. L. Li, H. X. Pan, W. P. Lin, Zhe Chu

arxiv:1604.08339 v2 · 2016-04-28 · 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{D2DIKFNDB42BDDAXHP6E6IJ2VP}

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	2026-05-18T01:07:50.736069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e868515a30f34118c173bfc4f213aabeaa3cd1c77d8db3dc0479527d517577c

Aliases

arxiv: 1604.08339 · arxiv_version: 1604.08339v2 · doi: 10.48550/arxiv.1604.08339 · pith_short_12: D2DIKFNDB42B · pith_short_16: D2DIKFNDB42BDDAX · pith_short_8: D2DIKFND

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/D2DIKFNDB42BDDAXHP6E6IJ2VP \
  | 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: 1e868515a30f34118c173bfc4f213aabeaa3cd1c77d8db3dc0479527d517577c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e440bd461d42eaf96f2ff6e28b30cba625957d4d6c2e9d408bb8200a8db5622",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2016-04-28T08:13:45Z",
    "title_canon_sha256": "375b0585d3bd03eff39d192fe0bf434d54d0f19b14f41714ac7d19b6ead54c7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.08339",
    "kind": "arxiv",
    "version": 2
  }
}