Pith Number

pith:WEXJV5GP

pith:2016:WEXJV5GPVBTOTKMJSPFS5HCUAG

not attested not anchored not stored refs pending

Sobolev type inequalities, Euler-Hilbert-Sobolev and Sobolev-Lorentz-Zygmund spaces on homogeneous groups

Durvudkhan Suragan, Michael Ruzhansky, Nurgissa Yessirkegenov

arxiv:1610.03379 v3 · 2016-10-11 · 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{WEXJV5GPVBTOTKMJSPFS5HCUAG}

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.

Receipt and verification

First computed	2026-05-18T00:25:21.291025Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b12e9af4cfa866e9a98993cb2e9c5401bf23c443697c1360f7ccaa1ba35b71bc

Aliases

arxiv: 1610.03379 · arxiv_version: 1610.03379v3 · doi: 10.48550/arxiv.1610.03379 · pith_short_12: WEXJV5GPVBTO · pith_short_16: WEXJV5GPVBTOTKMJ · pith_short_8: WEXJV5GP

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/WEXJV5GPVBTOTKMJSPFS5HCUAG \
  | 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: b12e9af4cfa866e9a98993cb2e9c5401bf23c443697c1360f7ccaa1ba35b71bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52c99494a7f32e25a625da869bd652ad64c5941fb874e473c5406fdcc35e02dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-10-11T14:58:49Z",
    "title_canon_sha256": "2fbea7cdbd57a3c23f62dc5bd611456a5ab66914517c6b919f4ce3acc5375fdb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.03379",
    "kind": "arxiv",
    "version": 3
  }
}