Pith Number

pith:5VSKWRG6

pith:2016:5VSKWRG66QIJNHUPAS56UGL7KA

not attested not anchored not stored refs pending

The boundedness of operators in Muckenhoupt weighted Morrey spaces via extrapolation techniques and duality

Hans-Juergen Schmeisser, Marcel Rosenthal

arxiv:1606.06584 v2 · 2016-06-21 · 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{5VSKWRG66QIJNHUPAS56UGL7KA}

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	2026-05-18T01:11:01.720372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed64ab44def410969e8f04bbea197f50233496ef986b4355b125a6888e3d842a

Aliases

arxiv: 1606.06584 · arxiv_version: 1606.06584v2 · doi: 10.48550/arxiv.1606.06584 · pith_short_12: 5VSKWRG66QIJ · pith_short_16: 5VSKWRG66QIJNHUP · pith_short_8: 5VSKWRG6

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/5VSKWRG66QIJNHUPAS56UGL7KA \
  | 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: ed64ab44def410969e8f04bbea197f50233496ef986b4355b125a6888e3d842a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c168d3bf84e6870a8c134cecd1085f9735c7b7883a0c1656bfd5828a50d5705b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-06-21T14:15:42Z",
    "title_canon_sha256": "6d46b93628a287fcde483a986de1926d730885b23755da2cbe8fa9e2fb789a47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.06584",
    "kind": "arxiv",
    "version": 2
  }
}