Pith Number

pith:QPMFHDCT

pith:2012:QPMFHDCTBGCYOMCW3JH6JRJVNZ

not attested not anchored not stored refs pending

Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals

Carlos P\'erez, Michael T. Lacey, Tuomas P. Hyt\"onen

arxiv:1202.2229 v1 · 2012-02-10 · 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{QPMFHDCTBGCYOMCW3JH6JRJVNZ}

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	2026-05-18T01:33:58.926193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83d8538c530985873056da4fe4c5356e72bb0c682f9d5819aed48cf5cd8f4b3b

Aliases

arxiv: 1202.2229 · arxiv_version: 1202.2229v1 · doi: 10.48550/arxiv.1202.2229 · pith_short_12: QPMFHDCTBGCY · pith_short_16: QPMFHDCTBGCYOMCW · pith_short_8: QPMFHDCT

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/QPMFHDCTBGCYOMCW3JH6JRJVNZ \
  | 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: 83d8538c530985873056da4fe4c5356e72bb0c682f9d5819aed48cf5cd8f4b3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0f6b7b59d803add371ddc3ba1a643ab9c13f35b0ec2f680c30c76df417c4070",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-02-10T10:12:18Z",
    "title_canon_sha256": "74fe60d4e64a045fc52702dbea660ab03b346cc3ba732802f7d8fa28b04ee8cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.2229",
    "kind": "arxiv",
    "version": 1
  }
}