Pith Number

pith:X7XYL634

pith:2025:X7XYL6347VXRYIW3H74LXNE6CS

not attested not anchored not stored refs pending

Besov--Triebel--Lizorkin-Type Spaces with Matrix $A_\infty$ Weights

Dachun Yang, Fan Bu, Tuomas Hyt\"onen, Wen Yuan

arxiv:2501.03050 v1 · 2025-01-06 · 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{X7XYL6347VXRYIW3H74LXNE6CS}

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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

Weighted Bourgain-Morrey-Besov type and Triebel-Lizorkin type spaces associated with operators

Receipt and verification

First computed	2026-07-05T09:57:29.877312Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfef85fb7cfd6f1c22db3ff8bbb49e149c317af0a7f45061f3445cc36001f90a

Aliases

arxiv: 2501.03050 · arxiv_version: 2501.03050v1 · doi: 10.48550/arxiv.2501.03050 · pith_short_12: X7XYL6347VXR · pith_short_16: X7XYL6347VXRYIW3 · pith_short_8: X7XYL634

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/X7XYL6347VXRYIW3H74LXNE6CS \
  | 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: bfef85fb7cfd6f1c22db3ff8bbb49e149c317af0a7f45061f3445cc36001f90a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4155988b405c9cfbb02907ce698ecc5f0ce317237c8fd6f42726e2aeda0eb102",
    "cross_cats_sorted": [
      "math.AP",
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-01-06T14:38:23Z",
    "title_canon_sha256": "57e30e8d7c336f6ae59d105120f522cccd9e05d8a7c01cb5c925ae6fd621b90f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.03050",
    "kind": "arxiv",
    "version": 1
  }
}