Pith Number

pith:GTWFMGMB

pith:2012:GTWFMGMBKP3C2Z4XQCYKOISPZQ

not attested not anchored not stored refs pending

The Cauchy Singular Integral Operator on Weighted Variable Lebesgue Spaces

Alexei Yu. Karlovich, Ilya M. Spitkovsky

arxiv:1202.2226 v1 · 2012-02-10 · math.FA · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GTWFMGMBKP3C2Z4XQCYKOISPZQ}

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	2026-05-18T04:02:36.877453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34ec56198153f62d679780b0a7224fcc347277637a3c3811e242a4ccaa1264a6

Aliases

arxiv: 1202.2226 · arxiv_version: 1202.2226v1 · doi: 10.48550/arxiv.1202.2226 · pith_short_12: GTWFMGMBKP3C · pith_short_16: GTWFMGMBKP3C2Z4X · pith_short_8: GTWFMGMB

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/GTWFMGMBKP3C2Z4XQCYKOISPZQ \
  | 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: 34ec56198153f62d679780b0a7224fcc347277637a3c3811e242a4ccaa1264a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0efb8621d4f2fcd36419fd1cc7e85f84a925db5b31e16ee95e7bdec7baed7f4",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-02-10T10:06:16Z",
    "title_canon_sha256": "5b6db7bb4e111af61c17d54f69e940664ab60a488fbe17bb27d7cfac7e8dbc76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.2226",
    "kind": "arxiv",
    "version": 1
  }
}