Pith Number

pith:QWO5XX6Y

pith:2018:QWO5XX6YC2BHWIFZ2NXXC7WR4T

not attested not anchored not stored refs pending

Atomic and Littlewood-Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications

Dachun Yang, Jun Liu, Long Huang, Wen Yuan

arxiv:1801.06251 v2 · 2018-01-18 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QWO5XX6YC2BHWIFZ2NXXC7WR4T}

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	2026-05-18T00:25:23.084938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

859ddbdfd816827b20b9d36f717ed1e4e378dc6af82afd7ae4535a585561fc1b

Aliases

arxiv: 1801.06251 · arxiv_version: 1801.06251v2 · doi: 10.48550/arxiv.1801.06251 · pith_short_12: QWO5XX6YC2BH · pith_short_16: QWO5XX6YC2BHWIFZ · pith_short_8: QWO5XX6Y

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/QWO5XX6YC2BHWIFZ2NXXC7WR4T \
  | 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: 859ddbdfd816827b20b9d36f717ed1e4e378dc6af82afd7ae4535a585561fc1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b204e321ae3a6ff88a7abcf9bb45665be58f2bf76d80201e85a64d56fed7a68b",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-01-18T23:34:18Z",
    "title_canon_sha256": "338e89bb28ed2b74b02dae290a55fc4822c1c04e657dd1f1a379a2844473ff1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.06251",
    "kind": "arxiv",
    "version": 2
  }
}