Pith Number

pith:JWX64L6R

pith:2011:JWX64L6R2NEABP2BIGQTJ6UQGY

not attested not anchored not stored refs pending

Quadratic $A_1$ bounds for commutators of singular integrals with BMO functions

Carmen Ortiz-Caraballo

arxiv:1104.1069 v1 · 2011-04-06 · 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{JWX64L6R2NEABP2BIGQTJ6UQGY}

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	2026-05-18T04:24:53.685021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4dafee2fd1d34800bf4141a134fa90360ac2d035ceb1703af3f221986947bf21

Aliases

arxiv: 1104.1069 · arxiv_version: 1104.1069v1 · doi: 10.48550/arxiv.1104.1069 · pith_short_12: JWX64L6R2NEA · pith_short_16: JWX64L6R2NEABP2B · pith_short_8: JWX64L6R

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/JWX64L6R2NEABP2BIGQTJ6UQGY \
  | 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: 4dafee2fd1d34800bf4141a134fa90360ac2d035ceb1703af3f221986947bf21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fae967a7e1b5b0108d48e3bd7835c7876230ab5bd711a0c76e48a292accda7a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-04-06T11:50:57Z",
    "title_canon_sha256": "a8f7ae9de7bfce479ab648c974809eac8ac55f84da7df94ad6ac011c92e6c152"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.1069",
    "kind": "arxiv",
    "version": 1
  }
}