Pith Number

pith:T564U5IU

pith:2011:T564U5IUM43GXAHAYFWN2XBHTS

not attested not anchored not stored refs pending

The $s$-Riesz transform of an $s$-dimensional measure in $\R^2$ is unbounded for $1<s<2$

Alexander Volberg, Fedor Nazarov, Vladimir Eiderman

arxiv:1109.2260 v3 · 2011-09-10 · math.AP · math.CA · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T564U5IUM43GXAHAYFWN2XBHTS}

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	2026-05-18T04:00:26.615574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f7dca751467366b80e0c16cdd5c279ca5559c7a997ec698147943e48775f026

Aliases

arxiv: 1109.2260 · arxiv_version: 1109.2260v3 · doi: 10.48550/arxiv.1109.2260 · pith_short_12: T564U5IUM43G · pith_short_16: T564U5IUM43GXAHA · pith_short_8: T564U5IU

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/T564U5IUM43GXAHAYFWN2XBHTS \
  | 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: 9f7dca751467366b80e0c16cdd5c279ca5559c7a997ec698147943e48775f026

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af78ac3cd12fbbc2f8ea887197d436eac94d7fdb385882123dd82c51dcd06979",
    "cross_cats_sorted": [
      "math.CA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-09-10T21:11:35Z",
    "title_canon_sha256": "cb7fc5dc4ff4176c7fbcaebe1e93a41ff1a9c9d88a18ca07b62c97a2a4a2914c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.2260",
    "kind": "arxiv",
    "version": 3
  }
}