Pith Number

pith:PLJ243SO

pith:2016:PLJ243SOPPHXLT4F2G6DP2ABUW

not attested not anchored not stored refs pending

On uniform boundedness of dyadic averaging operators in spaces of Hardy-Sobolev type

Andreas Seeger, Gustavo Garrig\'os, Tino Ullrich

arxiv:1610.04145 v2 · 2016-10-13 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PLJ243SOPPHXLT4F2G6DP2ABUW}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:49:51.498609Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ad3ae6e4e7bcf75cf85d1bc37e801a5a9a07e25447a5725d6f4cf491d9de2e5

Aliases

arxiv: 1610.04145 · arxiv_version: 1610.04145v2 · doi: 10.48550/arxiv.1610.04145 · pith_short_12: PLJ243SOPPHX · pith_short_16: PLJ243SOPPHXLT4F · pith_short_8: PLJ243SO

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/PLJ243SOPPHXLT4F2G6DP2ABUW \
  | 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: 7ad3ae6e4e7bcf75cf85d1bc37e801a5a9a07e25447a5725d6f4cf491d9de2e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d25dc0a9dcb5aa29caa92fbfe4787b3874fa0251707f010bd5333a874828ef4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-10-13T15:57:03Z",
    "title_canon_sha256": "2274a2c55cd612670e059583654984f636cc6e1fcd90a4fd8a56cb1c5eb6d4a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.04145",
    "kind": "arxiv",
    "version": 2
  }
}