Pith Number

pith:PZ6FRM4G

pith:2011:PZ6FRM4G5B65NCDHNN5YL5T2LL

not attested not anchored not stored refs pending

Logarithmic bump conditions and the two weight boundedness of Calder\'on-Zygmund operators

Alexander Reznikov, Alexander Volberg, David Cruz-Uribe

arxiv:1112.0676 v4 · 2011-12-03 · math.AP · 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{PZ6FRM4G5B65NCDHNN5YL5T2LL}

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	2026-05-18T03:37:19.080999Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e7c58b386e87dd688676b7b85f67a5ad9c73c8e0f30c2846708b375fcde203d

Aliases

arxiv: 1112.0676 · arxiv_version: 1112.0676v4 · doi: 10.48550/arxiv.1112.0676 · pith_short_12: PZ6FRM4G5B65 · pith_short_16: PZ6FRM4G5B65NCDH · pith_short_8: PZ6FRM4G

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/PZ6FRM4G5B65NCDHNN5YL5T2LL \
  | 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: 7e7c58b386e87dd688676b7b85f67a5ad9c73c8e0f30c2846708b375fcde203d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce82b4bf1fd3f4a13e27baed4042c28dacc0e0d4dd79b0d6b83bbea1390f52fa",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-12-03T17:28:42Z",
    "title_canon_sha256": "399648d043a1bfa59ffc8ba0888aa4baca431c7ba35f2f27ce4bf742989323e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0676",
    "kind": "arxiv",
    "version": 4
  }
}