Pith Number

pith:ETUIXFKO

pith:2018:ETUIXFKOGIF34Q47ZKXPGYZMON

not attested not anchored not stored refs pending

Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in $\mathbb Z^d$

B{\l}a\.zej Wr\'obel, Elias M. Stein, Jean Bourgain, Mariusz Mirek

arxiv:1804.07679 v2 · 2018-04-20 · math.CA · math.FA

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ETUIXFKOGIF34Q47ZKXPGYZMON}

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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.

Cited by

1 paper in Pith

Vector-valued $q$-variational inequalities for averaging operators and Hilbert transform

Receipt and verification

First computed	2026-05-17T23:48:22.746783Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24e88b954e320bbe439fcaaef3632c7356cabfc5f9da877e175518acdd73b718

Aliases

arxiv: 1804.07679 · arxiv_version: 1804.07679v2 · doi: 10.48550/arxiv.1804.07679 · pith_short_12: ETUIXFKOGIF3 · pith_short_16: ETUIXFKOGIF34Q47 · pith_short_8: ETUIXFKO

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/ETUIXFKOGIF34Q47ZKXPGYZMON \
  | 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: 24e88b954e320bbe439fcaaef3632c7356cabfc5f9da877e175518acdd73b718

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b91f80c4d1c8c62dd963733d0bf9be26d150a3c30ce5e57c93b14048b43e66b",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-04-20T15:34:33Z",
    "title_canon_sha256": "21d35e79a54d84d2758fc883d731ee93c4ab8e7e6ad633cbd6a52f7d2524bbc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.07679",
    "kind": "arxiv",
    "version": 2
  }
}