Pith Number

pith:GZAVCP4N

pith:2012:GZAVCP4NDN3T74T5PQLTISDURJ

not attested not anchored not stored refs pending

Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

Alexandre Almeida, Peter H\"ast\"o, Petteri Harjulehto, Teemu Lukkari

arxiv:1211.1495 v2 · 2012-11-07 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GZAVCP4NDN3T74T5PQLTISDURJ}

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	2026-05-18T03:09:22.709800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3641513f8d1b773ff27d7c173448748a759fdd648738b105b7baf4895d39f9ba

Aliases

arxiv: 1211.1495 · arxiv_version: 1211.1495v2 · doi: 10.48550/arxiv.1211.1495 · pith_short_12: GZAVCP4NDN3T · pith_short_16: GZAVCP4NDN3T74T5 · pith_short_8: GZAVCP4N

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/GZAVCP4NDN3T74T5PQLTISDURJ \
  | 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: 3641513f8d1b773ff27d7c173448748a759fdd648738b105b7baf4895d39f9ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22d398e225e084ccf690a7c6af5b8768f48b25bae5274e87a1ba1c959400df7c",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-11-07T09:45:15Z",
    "title_canon_sha256": "bc87682df2fd7087e0577c59262d82656f13643edf3642849cb1f162640c62c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1495",
    "kind": "arxiv",
    "version": 2
  }
}