Pith Number

pith:ZV4KMETS

pith:2024:ZV4KMETSECD42FY42HVVN3QBCA

not attested not anchored not stored refs pending

Optimal embedding results for fractional Sobolev spaces

Caterina Sportelli, Edoardo Proietti Lippi, Enrico Valdinoci, Serena Dipierro

arxiv:2411.12245 v1 · 2024-11-19 · 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{ZV4KMETSECD42FY42HVVN3QBCA}

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

2 papers in Pith

Regularity of superposition operators of mixed fractional order

Stability of the ball in isoperimetric inequalities between two fractional perimeters

Receipt and verification

First computed	2026-07-05T09:37:18.376766Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd78a612722087cd171cd1eb56ee011012533f4f27eabcf851ecde62aa21516d

Aliases

arxiv: 2411.12245 · arxiv_version: 2411.12245v1 · doi: 10.48550/arxiv.2411.12245 · pith_short_12: ZV4KMETSECD4 · pith_short_16: ZV4KMETSECD42FY4 · pith_short_8: ZV4KMETS

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/ZV4KMETSECD42FY42HVVN3QBCA \
  | 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: cd78a612722087cd171cd1eb56ee011012533f4f27eabcf851ecde62aa21516d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1e1a414497631f95114f6eba11f160125bb0ad247bcf227c2571cdf1322876d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-11-19T05:50:55Z",
    "title_canon_sha256": "6b8c9cf96e5db6dd114cb2ccda709e233dbd5b50e4cb7b1550653bd7f7401709"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.12245",
    "kind": "arxiv",
    "version": 1
  }
}