Pith Number

pith:VA745PF5

pith:2012:VA745PF5GALAVQH5RQ3E4YGLLX

not attested not anchored not stored refs pending

Boundedness of Commutators of Singular and Potential Operators in Generalized Grand Morrey Spaces and some applications

Alexander Meskhi, Humberto Rafeiro, Vakhtang Kokilashvili

arxiv:1205.6709 v1 · 2012-05-30 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VA745PF5GALAVQH5RQ3E4YGLLX}

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	2026-05-18T03:54:38.089223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a83fcebcbd30160ac0fd8c364e60cb5dd741831ff2c573298fab0564150e6e53

Aliases

arxiv: 1205.6709 · arxiv_version: 1205.6709v1 · doi: 10.48550/arxiv.1205.6709 · pith_short_12: VA745PF5GALA · pith_short_16: VA745PF5GALAVQH5 · pith_short_8: VA745PF5

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/VA745PF5GALAVQH5RQ3E4YGLLX \
  | 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: a83fcebcbd30160ac0fd8c364e60cb5dd741831ff2c573298fab0564150e6e53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfeb4844d66d9bc6b71defbd884972da09d962ea269ac43060b483f9b9521917",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-05-30T14:50:30Z",
    "title_canon_sha256": "2b9fda679b5a091c136362c3db128b8d8d9aefe5669e230ef69acdf808f2abe0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.6709",
    "kind": "arxiv",
    "version": 1
  }
}