Pith Number

pith:2PP2QKZB

pith:2009:2PP2QKZBDX3AZADF6KYNA5GMRR

not attested not anchored not stored refs pending

Separating inner and outer contributions in gravitational lenses using the perturbative method

C. Alard

arxiv:0909.4468 v1 · 2009-09-24 · 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{2PP2QKZBDX3AZADF6KYNA5GMRR}

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	2026-05-18T02:11:37.989519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3dfa82b211df60c8065f2b0d074cc8c6176ef35b4292df032f0adb34ddbece5

Aliases

arxiv: 0909.4468 · arxiv_version: 0909.4468v1 · doi: 10.48550/arxiv.0909.4468 · pith_short_12: 2PP2QKZBDX3A · pith_short_16: 2PP2QKZBDX3AZADF · pith_short_8: 2PP2QKZB

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/2PP2QKZBDX3AZADF6KYNA5GMRR \
  | 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: d3dfa82b211df60c8065f2b0d074cc8c6176ef35b4292df032f0adb34ddbece5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02e77f91ceed1d2a26e0912f4198ee49cbcde4417a2be1a3eb5b2233ae7bd045",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2009-09-24T15:56:18Z",
    "title_canon_sha256": "ac27088cb3b9ca3af552f8902be5ab6f619cc1ecbb1e0b51b49372ec9ae31f21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.4468",
    "kind": "arxiv",
    "version": 1
  }
}