Pith Number

pith:GK3Z7BHA

pith:2012:GK3Z7BHA7HZTFD2L6CWD2V3R64

not attested not anchored not stored refs pending

Littlewood--Paley--Rubio de Francia inequality in Morrey--Campanato spaces

Nikolay N. Osipov

arxiv:1211.0696 v2 · 2012-11-04 · 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{GK3Z7BHA7HZTFD2L6CWD2V3R64}

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	2026-05-18T03:29:50.691285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32b79f84e0f9f3328f4bf0ac3d5771f700636c02ab04c56163f6f2c7888b0eeb

Aliases

arxiv: 1211.0696 · arxiv_version: 1211.0696v2 · doi: 10.48550/arxiv.1211.0696 · pith_short_12: GK3Z7BHA7HZT · pith_short_16: GK3Z7BHA7HZTFD2L · pith_short_8: GK3Z7BHA

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/GK3Z7BHA7HZTFD2L6CWD2V3R64 \
  | 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: 32b79f84e0f9f3328f4bf0ac3d5771f700636c02ab04c56163f6f2c7888b0eeb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70f2bbb36e4a06360f126539aaeba4b0e07e617dfff8b8bf93d095683f8d08b6",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-11-04T15:50:27Z",
    "title_canon_sha256": "6dc47a8f793d44044f3c1c6e99169413e0933ed1bf72a993404f14c0cac0fb63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0696",
    "kind": "arxiv",
    "version": 2
  }
}