Pith Number

pith:SMYUOYDK

pith:2024:SMYUOYDKKWVLM63C6GSUCHGDBK

not attested not anchored not stored refs pending

Optimal stability of Hardy-Littlewood-Sobolev and Sobolev inequalities of arbitrary orders with dimension-dependent constants

Guozhen Lu, Hanli Tang, Lu Chen

arxiv:2405.17727 v3 · 2024-05-28 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SMYUOYDKKWVLM63C6GSUCHGDBK}

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.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-07-05T10:49:44.726355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

933147606a55aab67b62f1a5411cc30aa584c53a6ec076f639a60e822ed6d6fe

Aliases

arxiv: 2405.17727 · arxiv_version: 2405.17727v3 · doi: 10.48550/arxiv.2405.17727 · pith_short_12: SMYUOYDKKWVL · pith_short_16: SMYUOYDKKWVLM63C · pith_short_8: SMYUOYDK

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/SMYUOYDKKWVLM63C6GSUCHGDBK \
  | 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: 933147606a55aab67b62f1a5411cc30aa584c53a6ec076f639a60e822ed6d6fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ea573e79059b7ca9cd0988e497620d62419736109115a3cb855f80de617d336",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-05-28T00:55:37Z",
    "title_canon_sha256": "e93c25c6403afec7c96ed3a4828d5a6bea5f92048bd1d7086e2c8f83a0db0675"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.17727",
    "kind": "arxiv",
    "version": 3
  }
}