Pith Number

pith:7AQUHNBC

pith:2012:7AQUHNBCPQWRCXEQHJZYTSYDUE

not attested not anchored not stored refs pending

Necessary and sufficient conditions for boundedness of commutators of the general fractional integral operators on weighted Morrey spaces

Fayou Zhao, Zengyan Si

arxiv:1203.4337 v1 · 2012-03-20 · 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{7AQUHNBCPQWRCXEQHJZYTSYDUE}

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	2026-05-18T03:59:39.322013Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f82143b4227c2d115c903a7389cb03a1136bbc04644d37c9d74d330dc14683f0

Aliases

arxiv: 1203.4337 · arxiv_version: 1203.4337v1 · doi: 10.48550/arxiv.1203.4337 · pith_short_12: 7AQUHNBCPQWR · pith_short_16: 7AQUHNBCPQWRCXEQ · pith_short_8: 7AQUHNBC

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/7AQUHNBCPQWRCXEQHJZYTSYDUE \
  | 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: f82143b4227c2d115c903a7389cb03a1136bbc04644d37c9d74d330dc14683f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0633e4055086014493b40aa1e929e6661c10fef03b2d237c4d149a49047d4b4b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-03-20T08:24:56Z",
    "title_canon_sha256": "5841f775174aa44af529545eb1643ca39aa5bb06fa1c0d481a359d5708709474"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4337",
    "kind": "arxiv",
    "version": 1
  }
}