Pith Number

pith:ZUZ5ONKN

pith:2019:ZUZ5ONKNVWALJFT3ATPXIJLKLV

not attested not anchored not stored refs pending

Sobolev embeddings, extrapolations, and related inequalities

Oscar Dom\'inguez, Sergey Tikhonov

arxiv:1909.12818 v3 · 2019-09-27 · 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{ZUZ5ONKNVWALJFT3ATPXIJLKLV}

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 Brezis--Seeger--Van Schaftingen--Yung Formulae for Higher-Order Gradients in Ball Banach Function Spaces

Receipt and verification

First computed	2026-07-05T01:45:18.721391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd33d7354dad80b4967b04df74256a5d67a6d900b1d2968010e5ddb518e23f3b

Aliases

arxiv: 1909.12818 · arxiv_version: 1909.12818v3 · doi: 10.48550/arxiv.1909.12818 · pith_short_12: ZUZ5ONKNVWAL · pith_short_16: ZUZ5ONKNVWALJFT3 · pith_short_8: ZUZ5ONKN

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/ZUZ5ONKNVWALJFT3ATPXIJLKLV \
  | 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: cd33d7354dad80b4967b04df74256a5d67a6d900b1d2968010e5ddb518e23f3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0df8d356878896a9d2a8b50f1c34ca6f47e8761a55783d6e373ef493bafcbf6a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-09-27T17:44:30Z",
    "title_canon_sha256": "0bfe82ee28d5b16b0875d272b99ed62a1f3bf34ecf28a39ef5360d5d2fcc536d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.12818",
    "kind": "arxiv",
    "version": 3
  }
}