Pith Number

pith:AQPZOJKA

pith:2015:AQPZOJKA7Q36PXZTGIGDUDSKZX

not attested not anchored not stored refs pending

Characterizations of Variable Exponent Hardy Spaces via Riesz Transforms

Ciqiang Zhuo, Dachun Yang, Eiichi Nakai

arxiv:1508.05456 v1 · 2015-08-22 · math.CA · 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{AQPZOJKA7Q36PXZTGIGDUDSKZX}

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	2026-05-18T01:34:53.902399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

041f972540fc37e7df33320c3a0e4acdfbfeb72bd017d4d5f1eb713ef9e0c15c

Aliases

arxiv: 1508.05456 · arxiv_version: 1508.05456v1 · doi: 10.48550/arxiv.1508.05456 · pith_short_12: AQPZOJKA7Q36 · pith_short_16: AQPZOJKA7Q36PXZT · pith_short_8: AQPZOJKA

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/AQPZOJKA7Q36PXZTGIGDUDSKZX \
  | 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: 041f972540fc37e7df33320c3a0e4acdfbfeb72bd017d4d5f1eb713ef9e0c15c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58b706401c5cd0d075ab937c2a207cd8efa8b22b9f75b22f7c4ba3e28b3350bb",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-08-22T02:21:01Z",
    "title_canon_sha256": "36b7545384fd3d3835c053f16d02aeea0543ae7ade3bd7892b6cb9db8cacf2e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05456",
    "kind": "arxiv",
    "version": 1
  }
}