Pith Number

pith:D5XVSVJ3

pith:2017:D5XVSVJ3PSXBD3LHFSYB6JIEIN

not attested not anchored not stored refs pending

A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin--Triebel spaces with mixed norms

Jon Johnsen, Winfried Sickel

arxiv:1702.00972 v1 · 2017-02-03 · 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{D5XVSVJ3PSXBD3LHFSYB6JIEIN}

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	2026-05-18T00:51:29.272403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f6f59553b7cae11ed672cb01f2504435ae163b96b728893aa70255ae78a64e5

Aliases

arxiv: 1702.00972 · arxiv_version: 1702.00972v1 · doi: 10.48550/arxiv.1702.00972 · pith_short_12: D5XVSVJ3PSXB · pith_short_16: D5XVSVJ3PSXBD3LH · pith_short_8: D5XVSVJ3

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/D5XVSVJ3PSXBD3LHFSYB6JIEIN \
  | 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: 1f6f59553b7cae11ed672cb01f2504435ae163b96b728893aa70255ae78a64e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b19707f3bb9da09d4766ac11ddf4b2ebfb2dd3e7e8228f685045087b9a5aacfb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-02-03T11:19:22Z",
    "title_canon_sha256": "f3953d8f26fa2ab0d4da3c19ff1b9b880d1dd77eff2c4ce6c3b59acaa399802d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.00972",
    "kind": "arxiv",
    "version": 1
  }
}