Pith Number

pith:TGG7RFUP

pith:2012:TGG7RFUPJJRKFJTF3CCWS4EI4J

not attested not anchored not stored refs pending

New Real-Variable Characterizations of Musielak-Orlicz Hardy Spaces

Dachun Yang, Jizheng Huang, Yiyu Liang

arxiv:1201.4062 v4 · 2012-01-19 · 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{TGG7RFUPJJRKFJTF3CCWS4EI4J}

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	2026-05-18T03:55:01.529265Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

998df8968f4a62a2a665d885697088e24ea712d8405c7b3fc8cec583f662f38e

Aliases

arxiv: 1201.4062 · arxiv_version: 1201.4062v4 · doi: 10.48550/arxiv.1201.4062 · pith_short_12: TGG7RFUPJJRK · pith_short_16: TGG7RFUPJJRKFJTF · pith_short_8: TGG7RFUP

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/TGG7RFUPJJRKFJTF3CCWS4EI4J \
  | 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: 998df8968f4a62a2a665d885697088e24ea712d8405c7b3fc8cec583f662f38e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31852fabf86011203ff2b425668647694f5484e3a3f73b3f5b1b82bb5fb5be3a",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-01-19T14:06:45Z",
    "title_canon_sha256": "1c348c7d1e25743a3fcc39f9fbf24e8b0c36defdd829d8b9798cb8dca783bd03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4062",
    "kind": "arxiv",
    "version": 4
  }
}