Pith Number

pith:PDPYCA3D

pith:2010:PDPYCA3DZ3BZACAJ6SQK3P3FVA

not attested not anchored not stored refs pending

Analytic approach to perturbed Einstein ring with elliptical NFW lens model

Kazuhiro Yamamoto (Hiroshima University), Yuta Habara

arxiv:1012.1957 v1 · 2010-12-09 · 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{PDPYCA3DZ3BZACAJ6SQK3P3FVA}

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	2026-05-18T02:04:31.253018Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78df810363cec3900809f4a0adbf65a81710a21e450f199fe2152f7003bac3e8

Aliases

arxiv: 1012.1957 · arxiv_version: 1012.1957v1 · doi: 10.48550/arxiv.1012.1957 · pith_short_12: PDPYCA3DZ3BZ · pith_short_16: PDPYCA3DZ3BZACAJ · pith_short_8: PDPYCA3D

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/PDPYCA3DZ3BZACAJ6SQK3P3FVA \
  | 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: 78df810363cec3900809f4a0adbf65a81710a21e450f199fe2152f7003bac3e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e638d5fc21d6a16576d30e69c55bc8d9e9504a87983c13d41db4a4ca212af9db",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2010-12-09T09:40:43Z",
    "title_canon_sha256": "cf3b3855dcf5cd9dfbcd9850ed67b92bb98a95b690d898b54e627c68f3a22179"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1957",
    "kind": "arxiv",
    "version": 1
  }
}