Pith Number

pith:NIYFCKAC

pith:2023:NIYFCKAC74LHCXCEMQ3BJ3BSHE

not attested not anchored not stored refs pending

On the stability of critical points of the Hardy-Littlewood-Sobolev inequality

Kuan Liu, Qian Zhang, Wenming Zou

arxiv:2306.15862 v2 · 2023-06-28 · math.AP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NIYFCKAC74LHCXCEMQ3BJ3BSHE}

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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

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

Receipt and verification

First computed	2026-07-05T06:30:46.789556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a30512802ff16715c44643614ec32392021c178311ae413bcc514e38108a06d

Aliases

arxiv: 2306.15862 · arxiv_version: 2306.15862v2 · doi: 10.48550/arxiv.2306.15862 · pith_short_12: NIYFCKAC74LH · pith_short_16: NIYFCKAC74LHCXCE · pith_short_8: NIYFCKAC

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/NIYFCKAC74LHCXCEMQ3BJ3BSHE \
  | 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: 6a30512802ff16715c44643614ec32392021c178311ae413bcc514e38108a06d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a8b4a79f1f4bd2a9020e45979bfa5f3c7e7594247ac9587bd15b974fc467636",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2023-06-28T01:31:15Z",
    "title_canon_sha256": "3658df5bdfe96428a0844762cbba63f060eddb450b9ea8f2c3e650331bab5486"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.15862",
    "kind": "arxiv",
    "version": 2
  }
}