Pith Number

pith:RTKFZI4Q

pith:2019:RTKFZI4QXXDLAUXELY2T5WTBYB

not attested not anchored not stored refs pending

Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood--Paley Characterizations and Real Interpolation

Dachun Yang, Songbai Wang, Wen Yuan, Yangyang Zhang

arxiv:1906.03653 v2 · 2019-06-09 · 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{RTKFZI4QXXDLAUXELY2T5WTBYB}

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	2026-05-17T23:42:02.081807Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8cd45ca390bdc6b052e45e353eda61c0759c2a580eb5006979b0444c5f0ae169

Aliases

arxiv: 1906.03653 · arxiv_version: 1906.03653v2 · doi: 10.48550/arxiv.1906.03653 · pith_short_12: RTKFZI4QXXDL · pith_short_16: RTKFZI4QXXDLAUXE · pith_short_8: RTKFZI4Q

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/RTKFZI4QXXDLAUXELY2T5WTBYB \
  | 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: 8cd45ca390bdc6b052e45e353eda61c0759c2a580eb5006979b0444c5f0ae169

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "967a870a2f0a53fe5d65d6e24b3f7d053db586a845446e86388cd0a9ce45a127",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-06-09T14:47:17Z",
    "title_canon_sha256": "1ef20a4eb3e6779bc91bde9f1c523bb367b69d96ed935509de0736cd8b5967e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.03653",
    "kind": "arxiv",
    "version": 2
  }
}