Pith Number

pith:BOTGE3TV

pith:2013:BOTGE3TVMPVCK6GQNMWLL66E3Y

not attested not anchored not stored refs pending

Boundedness of Intrinsic Littlewood-Paley Functions on Musielak-Orlicz Morrey and Campanato Spaces

Dachun Yang, Eiichi Nakai, Junqiang Zhang, Yiyu Liang

arxiv:1309.6512 v1 · 2013-09-25 · math.CA · 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{BOTGE3TVMPVCK6GQNMWLL66E3Y}

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	2026-05-18T03:12:20.789947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ba6626e7563ea2578d06b2cb5fbc4de0b92e06fd64dae460c653efb8fc317d2

Aliases

arxiv: 1309.6512 · arxiv_version: 1309.6512v1 · doi: 10.48550/arxiv.1309.6512 · pith_short_12: BOTGE3TVMPVC · pith_short_16: BOTGE3TVMPVCK6GQ · pith_short_8: BOTGE3TV

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/BOTGE3TVMPVCK6GQNMWLL66E3Y \
  | 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: 0ba6626e7563ea2578d06b2cb5fbc4de0b92e06fd64dae460c653efb8fc317d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e4b2d6eb3e66c9e15da6cb849bdbc07af14952e71047706097e9d78380501af",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-09-25T14:13:10Z",
    "title_canon_sha256": "e2f2e42f1387727b3ce3dc72b005bcdddd91ddbfb3e77e3c537682de0b6b340f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6512",
    "kind": "arxiv",
    "version": 1
  }
}