Pith Number

pith:O7DBHU52

pith:2012:O7DBHU52SI3B6GTOXRMO3XAMBA

not attested not anchored not stored refs pending

Quadrature by Expansion: A New Method for the Evaluation of Layer Potentials

Alexander Barnett, Andreas Kl\"ockner, Leslie Greengard, Michael O'Neil

arxiv:1207.4461 v2 · 2012-07-18 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O7DBHU52SI3B6GTOXRMO3XAMBA}

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	2026-05-18T01:56:16.699843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77c613d3ba92361f1a6ebc58eddc0c0827e40921366320aabea0a2eec260e617

Aliases

arxiv: 1207.4461 · arxiv_version: 1207.4461v2 · doi: 10.48550/arxiv.1207.4461 · pith_short_12: O7DBHU52SI3B · pith_short_16: O7DBHU52SI3B6GTO · pith_short_8: O7DBHU52

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/O7DBHU52SI3B6GTOXRMO3XAMBA \
  | 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: 77c613d3ba92361f1a6ebc58eddc0c0827e40921366320aabea0a2eec260e617

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "158b186991ce706955f318718e8eb1cd4bdc34a6e9fb6f8a7b3d559a49b9b918",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2012-07-18T19:39:15Z",
    "title_canon_sha256": "c82f8a2a8e5cf18c75ac3040575f02f08df510aafca980f3c9a01dee99b44b41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4461",
    "kind": "arxiv",
    "version": 2
  }
}