Pith Number

pith:TJVPBPYH

pith:2011:TJVPBPYH5WNAK7UHQGZCDTJYGP

not attested not anchored not stored refs pending

Mixed $A_p$-$A_r$ inequalities for classical singular integrals and Littlewood-Paley operators

Andrei K. Lerner

arxiv:1105.5735 v1 · 2011-05-28 · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TJVPBPYH5WNAK7UHQGZCDTJYGP}

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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	2026-05-18T04:21:01.677412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a6af0bf07ed9a057e8781b221cd3833fa6f044f4eea9b90410a56e2b8e928ca

Aliases

arxiv: 1105.5735 · arxiv_version: 1105.5735v1 · doi: 10.48550/arxiv.1105.5735 · pith_short_12: TJVPBPYH5WNA · pith_short_16: TJVPBPYH5WNAK7UH · pith_short_8: TJVPBPYH

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/TJVPBPYH5WNAK7UHQGZCDTJYGP \
  | 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: 9a6af0bf07ed9a057e8781b221cd3833fa6f044f4eea9b90410a56e2b8e928ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5772dd94540e8fca689aab46af194fbb2e2355dd72e8fe2778bbd56f803679e6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-05-28T18:44:17Z",
    "title_canon_sha256": "f2e6d44282b5e2f5cc19ec2e4a1892962e4d7b5c4de4e15273ebe02954163ebb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5735",
    "kind": "arxiv",
    "version": 1
  }
}