Pith Number

pith:7VAUUNWW

pith:2025:7VAUUNWWAFJW3QSUJSXMMQCD6E

not attested not anchored not stored refs pending

Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding

Dachun Yang, Fan Bu, Mingdong Zhang, Wen Yuan

arxiv:2505.02136 v1 · 2025-05-04 · math.FA · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7VAUUNWWAFJW3QSUJSXMMQCD6E}

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.

Cited by

1 paper in Pith

Matrix-Weighted Campanato Spaces: Duality and Calder\'on--Zygmund Operators

Receipt and verification

First computed	2026-07-05T10:58:32.577787Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd414a36d601536dc2544caec64043f11d1024ee7fe9bd1b51ddbc1efef52d4b

Aliases

arxiv: 2505.02136 · arxiv_version: 2505.02136v1 · doi: 10.48550/arxiv.2505.02136 · pith_short_12: 7VAUUNWWAFJW · pith_short_16: 7VAUUNWWAFJW3QSU · pith_short_8: 7VAUUNWW

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/7VAUUNWWAFJW3QSUJSXMMQCD6E \
  | 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: fd414a36d601536dc2544caec64043f11d1024ee7fe9bd1b51ddbc1efef52d4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f6bb8b3665b3877fe7bfe24042056f64091c5db2a2e5561d3990ed06635576a",
    "cross_cats_sorted": [
      "math.AP",
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-05-04T14:53:33Z",
    "title_canon_sha256": "f503631e9980e2e3c189d7db3f84456acb15eb30040e450ae67458ee756d01d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.02136",
    "kind": "arxiv",
    "version": 1
  }
}