Pith Number

pith:LMZG6JM3

pith:2016:LMZG6JM3L273TT6YUEKM2RRGDB

not attested not anchored not stored refs pending

A Revisit on Commutators of linear and bilinear Fractional Integral Operator

Mingming Cao, Qingying Xue

arxiv:1604.06992 v1 · 2016-04-24 · 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{LMZG6JM3L273TT6YUEKM2RRGDB}

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	2026-05-18T01:16:23.383541Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b326f259b5ebfb9cfd8a114cd4626187c2305a54d2e504a8720d9cf587292d2

Aliases

arxiv: 1604.06992 · arxiv_version: 1604.06992v1 · doi: 10.48550/arxiv.1604.06992 · pith_short_12: LMZG6JM3L273 · pith_short_16: LMZG6JM3L273TT6Y · pith_short_8: LMZG6JM3

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/LMZG6JM3L273TT6YUEKM2RRGDB \
  | 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: 5b326f259b5ebfb9cfd8a114cd4626187c2305a54d2e504a8720d9cf587292d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16ebedcc1576c28dd69ee0549e35587a19b508e39b57a40d4804d016c8915692",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-04-24T06:57:04Z",
    "title_canon_sha256": "298781d41f8d301f773e35542f1034133832307bd75de162386dd60798565ce9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.06992",
    "kind": "arxiv",
    "version": 1
  }
}