Pith Number

pith:CHFFU27B

pith:2008:CHFFU27BYDMQCY5HNL6MGBTYW3

not attested not anchored not stored refs pending

Multipole Formulae for Gravitational Lensing Shear and Flexion

Gary M. Bernstein, Reiko Nakajima

arxiv:0807.1931 v1 · 2008-07-11 · astro-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CHFFU27BYDMQCY5HNL6MGBTYW3}

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	2026-05-18T04:29:33.256638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11ca5a6be1c0d90163a76afcc30678b6d516a9585be6d2fd25c19627519529af

Aliases

arxiv: 0807.1931 · arxiv_version: 0807.1931v1 · doi: 10.48550/arxiv.0807.1931 · pith_short_12: CHFFU27BYDMQ · pith_short_16: CHFFU27BYDMQCY5H · pith_short_8: CHFFU27B

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/CHFFU27BYDMQCY5HNL6MGBTYW3 \
  | 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: 11ca5a6be1c0d90163a76afcc30678b6d516a9585be6d2fd25c19627519529af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0afa6b872c0fcbaaebceffdef8231a0c2f2a61f92dd810e7a8f8ef84a017d11",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph",
    "submitted_at": "2008-07-11T20:18:40Z",
    "title_canon_sha256": "8efe899bc7040fdf8f8837fc431d8f8665320dbdc4e44c0d764a486bc0073972"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.1931",
    "kind": "arxiv",
    "version": 1
  }
}