Pith Number

pith:QTRWS2OL

pith:2009:QTRWS2OLCU4KEUDKAVT7GDZ5AL

not attested not anchored not stored refs pending

Weak and Strong-type estimates for Haar Shift Operators: Sharp power on the $A_p$ characteristic

Armen Vagharshakyan, Maria Carmen Reguera, Michael T. Lacey, Tuomas P. Hyt\"onen

arxiv:0911.0713 v2 · 2009-11-03 · 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{QTRWS2OLCU4KEUDKAVT7GDZ5AL}

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	2026-05-18T04:25:37.934911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84e36969cb1538a2506a0567f30f3d02c8e946a98eaf2332d0f7c7b3447a5dbf

Aliases

arxiv: 0911.0713 · arxiv_version: 0911.0713v2 · doi: 10.48550/arxiv.0911.0713 · pith_short_12: QTRWS2OLCU4K · pith_short_16: QTRWS2OLCU4KEUDK · pith_short_8: QTRWS2OL

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/QTRWS2OLCU4KEUDKAVT7GDZ5AL \
  | 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: 84e36969cb1538a2506a0567f30f3d02c8e946a98eaf2332d0f7c7b3447a5dbf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0986ed8f65c5e0c369f2a8fef4f879a21a4e2dcbf5729bdad426b909b92ae72c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-11-03T23:53:10Z",
    "title_canon_sha256": "07bc1d75d16f367c14d92e5f7dae887b11b2b5ab01fb1485521db150eb095f62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.0713",
    "kind": "arxiv",
    "version": 2
  }
}