Pith Number

pith:CKQCWSON

pith:2016:CKQCWSON44YBKJVNFDPGQOWPCM

not attested not anchored not stored refs pending

Fractional integral operator for $L^1$ vector fields and its applications

Zhibing Zhang

arxiv:1602.05846 v2 · 2016-01-15 · math.CA · math.AP · 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{CKQCWSON44YBKJVNFDPGQOWPCM}

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	2026-05-17T23:50:07.677833Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12a02b49cde7301526ad28de683acf131cd1841d9deb7cf360af3e05180b3655

Aliases

arxiv: 1602.05846 · arxiv_version: 1602.05846v2 · doi: 10.48550/arxiv.1602.05846 · pith_short_12: CKQCWSON44YB · pith_short_16: CKQCWSON44YBKJVN · pith_short_8: CKQCWSON

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/CKQCWSON44YBKJVNFDPGQOWPCM \
  | 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: 12a02b49cde7301526ad28de683acf131cd1841d9deb7cf360af3e05180b3655

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc837ecead402956bccb614dc67f1c61511878fa54e36840c3457baf27177716",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-01-15T07:20:42Z",
    "title_canon_sha256": "8e6286ef5f2b0e06226f2dc537fb97c760f1addecff8062082239e654bb135d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.05846",
    "kind": "arxiv",
    "version": 2
  }
}