Pith Number

pith:KHCZSM7F

pith:2018:KHCZSM7FLCOVGSUETCVZLOJFRD

not attested not anchored not stored refs pending

Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and $p$-sub-Laplacian systems

Aidyn Kassymov, Durvudkhan Suragan, Michael Ruzhansky

arxiv:1806.08940 v1 · 2018-06-23 · 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{KHCZSM7FLCOVGSUETCVZLOJFRD}

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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.

Receipt and verification

First computed	2026-05-18T00:12:30.822076Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51c59933e5589d534a8498ab95b92588f483e04d376ef7a29586d77c383069d0

Aliases

arxiv: 1806.08940 · arxiv_version: 1806.08940v1 · doi: 10.48550/arxiv.1806.08940 · pith_short_12: KHCZSM7FLCOV · pith_short_16: KHCZSM7FLCOVGSUE · pith_short_8: KHCZSM7F

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/KHCZSM7FLCOVGSUETCVZLOJFRD \
  | 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: 51c59933e5589d534a8498ab95b92588f483e04d376ef7a29586d77c383069d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98da689dee583d20917a81220ffa4617ca6d51680e5b49ba3095e6a72a9bb9f0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-06-23T10:12:05Z",
    "title_canon_sha256": "db0297aa4b8b8d591503b9b9999849fd9a6b534924d5357e10f15020078b7d71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.08940",
    "kind": "arxiv",
    "version": 1
  }
}