Pith Number

pith:ZRZ2WXER

pith:2013:ZRZ2WXER6YUBOYDZQXJUGQ4QBQ

not attested not anchored not stored refs pending

On the boundedness of generalized Ces\`aro operators on Sobolev spaces

Carlos Lizama, Luis S\'anchez-Lajusticia, Pedro J. Miana, Rodrigo Ponce

arxiv:1304.1622 v1 · 2013-04-05 · 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{ZRZ2WXER6YUBOYDZQXJUGQ4QBQ}

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	2026-05-18T03:28:55.198867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc73ab5c91f62817607985d34343900c34c2c9359e65d10d31aab43a2ab0affa

Aliases

arxiv: 1304.1622 · arxiv_version: 1304.1622v1 · doi: 10.48550/arxiv.1304.1622 · pith_short_12: ZRZ2WXER6YUB · pith_short_16: ZRZ2WXER6YUBOYDZ · pith_short_8: ZRZ2WXER

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/ZRZ2WXER6YUBOYDZQXJUGQ4QBQ \
  | 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: cc73ab5c91f62817607985d34343900c34c2c9359e65d10d31aab43a2ab0affa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "342d10a20bdb6578a0807fa4402dc743308198d6995c49f6a7c726ecb6640887",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-04-05T06:34:33Z",
    "title_canon_sha256": "731f6f4ab60a13ee0c584255afa0ffc0c9b6ad996954a5ccd3369b33f7b2dd2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.1622",
    "kind": "arxiv",
    "version": 1
  }
}