Pith Number

pith:WRINWGST

pith:2016:WRINWGSTIER3S7NKHSC6HJF4SV

not attested not anchored not stored refs pending

Littlewood-Paley Characterizations of Anisotropic Hardy-Lorentz Spaces

Dachun Yang, Jun Liu, Wen Yuan

arxiv:1601.05242 v2 · 2016-01-20 · 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{WRINWGSTIER3S7NKHSC6HJF4SV}

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	2026-05-18T01:22:05.302384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b450db1a534123b97daa3c85e3a4bc9560205973570383ba0860b6eeae5ac050

Aliases

arxiv: 1601.05242 · arxiv_version: 1601.05242v2 · doi: 10.48550/arxiv.1601.05242 · pith_short_12: WRINWGSTIER3 · pith_short_16: WRINWGSTIER3S7NK · pith_short_8: WRINWGST

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/WRINWGSTIER3S7NKHSC6HJF4SV \
  | 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: b450db1a534123b97daa3c85e3a4bc9560205973570383ba0860b6eeae5ac050

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dcd84de1b75618ebd00ad5249e088ed1b50b822a6e844df1ab7fd9e8dd484e5",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-01-20T11:32:26Z",
    "title_canon_sha256": "2e78c8c53fb00911570877977fa69f93bad74669e159d5c97ea2f943c86410cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.05242",
    "kind": "arxiv",
    "version": 2
  }
}