Pith Number

pith:GIZFZT2L

pith:2019:GIZFZT2LT6KNAZDNXZX4I45FQ6

not attested not anchored not stored refs pending

Buerling-Ahlfors Commutators on Weighted Morrey Spaces and Applications to Beltrami Equations

Dachun Yang, Dongyong Yang, Jin Tao

arxiv:1908.08626 v1 · 2019-08-22 · math.CA · math.AP · 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{GIZFZT2LT6KNAZDNXZX4I45FQ6}

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	2026-07-04T23:59:16.228696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32325ccf4b9f94d0646dbe6fc473a587b6012e741e683b773243f75213eda751

Aliases

arxiv: 1908.08626 · arxiv_version: 1908.08626v1 · doi: 10.48550/arxiv.1908.08626 · pith_short_12: GIZFZT2LT6KN · pith_short_16: GIZFZT2LT6KNAZDN · pith_short_8: GIZFZT2L

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/GIZFZT2LT6KNAZDNXZX4I45FQ6 \
  | 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: 32325ccf4b9f94d0646dbe6fc473a587b6012e741e683b773243f75213eda751

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b95698776717756eb299ee2af5ede0eb89af743121e0c5cf07c29ad0c89b8987",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-08-22T23:57:53Z",
    "title_canon_sha256": "bb3bc579cd183a96503525f34d0915d119d9cbf3f80658718dc8d99454944ecc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08626",
    "kind": "arxiv",
    "version": 1
  }
}