Pith Number

pith:I2KMCKRO

pith:2025:I2KMCKROSJKBLLLNNU7HXGK2VZ

not attested not anchored not stored refs pending

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

Dachun Yang, Wen Yuan, Yiqun Chen

arxiv:2508.15195 v1 · 2025-08-21 · 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{I2KMCKROSJKBLLLNNU7HXGK2VZ}

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	2026-07-05T11:57:08.099989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4694c12a2e925415ad6d6d3e7b995aae4bbbe1552fdd25cd6bb630692990d613

Aliases

arxiv: 2508.15195 · arxiv_version: 2508.15195v1 · doi: 10.48550/arxiv.2508.15195 · pith_short_12: I2KMCKROSJKB · pith_short_16: I2KMCKROSJKBLLLN · pith_short_8: I2KMCKRO

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/I2KMCKROSJKBLLLNNU7HXGK2VZ \
  | 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: 4694c12a2e925415ad6d6d3e7b995aae4bbbe1552fdd25cd6bb630692990d613

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f91a62168addee9b1408c9707cab1f6877aed4cd0058dfbf7c8501a743ffad43",
    "cross_cats_sorted": [
      "math.AP",
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-08-21T03:08:04Z",
    "title_canon_sha256": "86909f1239d0c095deca367863fe7b636b7743d10d3c0a71a4a0e0df965126c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.15195",
    "kind": "arxiv",
    "version": 1
  }
}