Pith Number

pith:ATTTKVID

pith:2025:ATTTKVIDHNEF5GBAD5CC2KSVO4

not attested not anchored not stored refs pending

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

Jingshi Xu, Pengfei Guo, Tengfei Bai

arxiv:2505.19135 v1 · 2025-05-25 · math.FA · 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{ATTTKVIDHNEF5GBAD5CC2KSVO4}

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	2026-07-05T11:09:25.480052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04e73555033b485e98201f442d2a55773c037d145975b9e6db85ff899ae68f95

Aliases

arxiv: 2505.19135 · arxiv_version: 2505.19135v1 · doi: 10.48550/arxiv.2505.19135 · pith_short_12: ATTTKVIDHNEF · pith_short_16: ATTTKVIDHNEF5GBA · pith_short_8: ATTTKVID

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/ATTTKVIDHNEF5GBAD5CC2KSVO4 \
  | 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: 04e73555033b485e98201f442d2a55773c037d145975b9e6db85ff899ae68f95

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8339e5d3c526184d8a4c55974cd01f0b83f48bce87f1e7baa6dc8dd7430fe95",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-05-25T13:17:53Z",
    "title_canon_sha256": "263f5f2d9a95f3738d77ab276dc6d38153f5a248f7004be379b750a71b847eb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.19135",
    "kind": "arxiv",
    "version": 1
  }
}