Pith Number

pith:2OPJ34JC

pith:2025:2OPJ34JCPFRR2K4XGHBHMMH74U

not attested not anchored not stored refs pending

Sharp gradient stability for a class of Hardy-Sobolev-Maz'ya inequalities

An Zhang, Jingze Fu, Wei Dai

arxiv:2509.00814 v2 · 2025-08-31 · 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{2OPJ34JCPFRR2K4XGHBHMMH74U}

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	2026-05-29T01:04:55.560452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d39e9df12279631d2b9731c27630ffe51b0b68497cde175a0e5aed1c68050815

Aliases

arxiv: 2509.00814 · arxiv_version: 2509.00814v2 · doi: 10.48550/arxiv.2509.00814 · pith_short_12: 2OPJ34JCPFRR · pith_short_16: 2OPJ34JCPFRR2K4X · pith_short_8: 2OPJ34JC

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/2OPJ34JCPFRR2K4XGHBHMMH74U \
  | 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: d39e9df12279631d2b9731c27630ffe51b0b68497cde175a0e5aed1c68050815

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab38897b36fea0df01d241ab34661e46154fdd5945761da1eb023caae37c3174",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-08-31T12:15:41Z",
    "title_canon_sha256": "ddbba1ff759b48cda7832690402a53c49911cb56f8026eb786fa74df4905f46b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.00814",
    "kind": "arxiv",
    "version": 2
  }
}