Pith Number

pith:CBK3HQGK

pith:2010:CBK3HQGKFK3Y62IV5WMVKRU2KW

not attested not anchored not stored refs pending

End-point estimates for iterated commutators of multilinear singular integrals

Carlos Perez, Gladis Pradolini, Rodolfo Torres, Rodrigo Trujillo-Gonzalez

arxiv:1004.4976 v2 · 2010-04-28 · 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{CBK3HQGKFK3Y62IV5WMVKRU2KW}

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	2026-05-18T02:24:15.549925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1055b3c0ca2ab78f6915ed9955469a559814c2b40147ede0e3042c8a065b1ce8

Aliases

arxiv: 1004.4976 · arxiv_version: 1004.4976v2 · doi: 10.48550/arxiv.1004.4976 · pith_short_12: CBK3HQGKFK3Y · pith_short_16: CBK3HQGKFK3Y62IV · pith_short_8: CBK3HQGK

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/CBK3HQGKFK3Y62IV5WMVKRU2KW \
  | 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: 1055b3c0ca2ab78f6915ed9955469a559814c2b40147ede0e3042c8a065b1ce8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "872cd656fa6cd4df46c200bc1a32e32f36b4c5ffa1fa599098646fcb5737671e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-04-28T08:42:26Z",
    "title_canon_sha256": "f7e5fae83d8afc7dad60cbc4205fa5ccca55c920d03cd5cf38c98f3714f4ef2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4976",
    "kind": "arxiv",
    "version": 2
  }
}