Pith Number

pith:X32EQZFE

pith:2019:X32EQZFEOMLKOFW76R5SBJD2BK

not attested not anchored not stored refs pending

Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces I: Decompositions with Applications to Boundedness of Calder\'on--Zygmund Operators

Dachun Yang, Songbai Wang, Wen Yuan, Yangyang Zhang

arxiv:1905.02097 v2 · 2019-05-06 · math.CA · math.AP · 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{X32EQZFEOMLKOFW76R5SBJD2BK}

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	2026-05-17T23:42:02.226805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bef44864a47316a716dff47b20a47a0ab047c8a55dbdcd0606ba0e81c2fe070c

Aliases

arxiv: 1905.02097 · arxiv_version: 1905.02097v2 · doi: 10.48550/arxiv.1905.02097 · pith_short_12: X32EQZFEOMLK · pith_short_16: X32EQZFEOMLKOFW7 · pith_short_8: X32EQZFE

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/X32EQZFEOMLKOFW76R5SBJD2BK \
  | 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: bef44864a47316a716dff47b20a47a0ab047c8a55dbdcd0606ba0e81c2fe070c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c4e44dc2393484626a9d22822b13c1754197eec8d3ab9280a09d8f2945caa7e",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-05-06T15:21:32Z",
    "title_canon_sha256": "fd6500261e1644d0b06a8cbb5b2aafb7b0d99ada10b9ef9c1140093adcbbaf1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.02097",
    "kind": "arxiv",
    "version": 2
  }
}