Pith Number

pith:7VTVOQZX

pith:2026:7VTVOQZXXDJDF4663VKMLRG6SN

not attested not anchored not stored refs pending

Fractional Leibniz rules for the Dunkl Laplacian in Besov and Triebel--Lizorkin spaces

Suman Mukherjee, The Anh Bui, Xueting Han

arxiv:2605.29406 v1 · 2026-05-28 · math.AP · 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{7VTVOQZXXDJDF4663VKMLRG6SN}

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	2026-05-29T01:05:37.310503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd67574337b8d232f3dedd54c5c4de9346ce96d1d7892dbc01a7342aebe88e2a

Aliases

arxiv: 2605.29406 · arxiv_version: 2605.29406v1 · doi: 10.48550/arxiv.2605.29406 · pith_short_12: 7VTVOQZXXDJD · pith_short_16: 7VTVOQZXXDJDF466 · pith_short_8: 7VTVOQZX

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/7VTVOQZXXDJDF4663VKMLRG6SN \
  | 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: fd67574337b8d232f3dedd54c5c4de9346ce96d1d7892dbc01a7342aebe88e2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5f8c9d41d14b261790c5d6abb026fabcad59d9e97768505258456c7da8e6d4c",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-28T05:58:47Z",
    "title_canon_sha256": "fd9c7c368d9c55bbb1bc77dccbe59a35163f950b2c8183f0af7131aa30ed59c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.29406",
    "kind": "arxiv",
    "version": 1
  }
}