Pith Number

pith:LISXRTW2

pith:2014:LISXRTW2IQV7DPDRSZXWHZ7CTV

not attested not anchored not stored refs pending

The strongest gravitational lenses: III. The order statistics of the largest Einstein radii

Jean-Claude Waizmann, Massimo Meneghetti, Matthias Bartelmann, Matthias Redlich

arxiv:1403.4573 v1 · 2014-03-18 · 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{LISXRTW2IQV7DPDRSZXWHZ7CTV}

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	2026-05-18T02:52:25.297792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a2578ceda442bf1bc71966f63e7e29d677458a5f7146b1edd64d8d664cd0125

Aliases

arxiv: 1403.4573 · arxiv_version: 1403.4573v1 · doi: 10.48550/arxiv.1403.4573 · pith_short_12: LISXRTW2IQV7 · pith_short_16: LISXRTW2IQV7DPDR · pith_short_8: LISXRTW2

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/LISXRTW2IQV7DPDRSZXWHZ7CTV \
  | 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: 5a2578ceda442bf1bc71966f63e7e29d677458a5f7146b1edd64d8d664cd0125

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a91cce9c27242f18607bea8a10644580894c22551a74f8a5a2d6bcf95595a9f1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2014-03-18T18:52:36Z",
    "title_canon_sha256": "e3185147b26443698f90df55318eecf7c65512ea56a6fb469154b4629b5004af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.4573",
    "kind": "arxiv",
    "version": 1
  }
}