Pith Number

pith:XEQQ3GGQ

pith:2016:XEQQ3GGQWDHMW57V7BC3N7B6KQ

not attested not anchored not stored refs pending

Characterization of CMO via compactness of the commutators of bilinear fractional integral operators

Dinghuai Wang, Jiang Zhou, Wenyi Chen

arxiv:1612.01116 v1 · 2016-12-04 · 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{XEQQ3GGQWDHMW57V7BC3N7B6KQ}

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	2026-05-18T00:55:53.317920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9210d98d0b0cecb77f5f845b6fc3e541417d68db6f91078b797307e8e2f05a4

Aliases

arxiv: 1612.01116 · arxiv_version: 1612.01116v1 · doi: 10.48550/arxiv.1612.01116 · pith_short_12: XEQQ3GGQWDHM · pith_short_16: XEQQ3GGQWDHMW57V · pith_short_8: XEQQ3GGQ

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/XEQQ3GGQWDHMW57V7BC3N7B6KQ \
  | 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: b9210d98d0b0cecb77f5f845b6fc3e541417d68db6f91078b797307e8e2f05a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a149c0ae97b6cd65e956bfc85ebc12604574193f6b12f34a529069545eb89ab7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-12-04T13:17:21Z",
    "title_canon_sha256": "e8fab266f25bfd5002e1917d8c97c296ce3e2eb7f6378951681f51f2aad0a58b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.01116",
    "kind": "arxiv",
    "version": 1
  }
}