Pith Number

pith:FFBLVESR

pith:2010:FFBLVESRLB5QGE62HEEXFAEXIB

not attested not anchored not stored refs pending

Equivalent Characterizations for Boundedness of Maximal Singular Integrals on $ax+b$\,--Groups

Dachun Yang, Liguang Liu, Maria Vallarino

arxiv:1008.0043 v2 · 2010-07-31 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FFBLVESRLB5QGE62HEEXFAEXIB}

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	2026-05-18T04:17:03.283322Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2942ba9251587b0313da39097280974065ca9f9f1593e5acb870efce9330a719

Aliases

arxiv: 1008.0043 · arxiv_version: 1008.0043v2 · doi: 10.48550/arxiv.1008.0043 · pith_short_12: FFBLVESRLB5Q · pith_short_16: FFBLVESRLB5QGE62 · pith_short_8: FFBLVESR

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/FFBLVESRLB5QGE62HEEXFAEXIB \
  | 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: 2942ba9251587b0313da39097280974065ca9f9f1593e5acb870efce9330a719

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3d037df013e03d179934a8b32ee98c94cc7786fc90cca9b453c1110502fae9c",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-07-31T02:17:01Z",
    "title_canon_sha256": "c9c0077cee60161d16d881ddf23d772a041a4171fccb34bfd54de30fcf0dc704"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.0043",
    "kind": "arxiv",
    "version": 2
  }
}