Pith Number

pith:HN6254Z2

pith:2011:HN6254Z27GKMVLO6QE5SHW5JB5

not attested not anchored not stored refs pending

Sharp Estimates for $p$-Adic Hardy, Hardy-Littlewood-P\'olya Operators and Commutators

Qingyan Wu, Shanzhen Lu, Zunwei Fu

arxiv:1105.2888 v1 · 2011-05-14 · 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{HN6254Z27GKMVLO6QE5SHW5JB5}

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	2026-05-18T04:22:01.819307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b7daef33af994caadde813b23dba90f7d15ad90f805c8c7281df19a50356ce9

Aliases

arxiv: 1105.2888 · arxiv_version: 1105.2888v1 · doi: 10.48550/arxiv.1105.2888 · pith_short_12: HN6254Z27GKM · pith_short_16: HN6254Z27GKMVLO6 · pith_short_8: HN6254Z2

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/HN6254Z27GKMVLO6QE5SHW5JB5 \
  | 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: 3b7daef33af994caadde813b23dba90f7d15ad90f805c8c7281df19a50356ce9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e414fbe7c2e1224767e0ff66e333d94dd7a87d559b0db2b4cf5c8bb5dc05b37f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-05-14T11:12:09Z",
    "title_canon_sha256": "7cb46ca6e9af32d1b85b42b6f07c4547a800878b72808eae40489e5f0a9f3237"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2888",
    "kind": "arxiv",
    "version": 1
  }
}