Pith Number

pith:PKFTBC4S

pith:2019:PKFTBC4S47CAVEGG232RL5W52U

not attested not anchored not stored refs pending

Some embeddings of Morrey spaces with critical smoothness

Dorothee D. Haroske, Leszek Skrzypczak, Susana D. Moura

arxiv:1905.09703 v1 · 2019-05-23 · math.FA · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PKFTBC4S47CAVEGG232RL5W52U}

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	2026-05-17T23:45:16.281797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a8b308b92e7c40a90c6d6f515f6ddd51fa719ffc9bb08ed7e0b3087e4f0445d

Aliases

arxiv: 1905.09703 · arxiv_version: 1905.09703v1 · doi: 10.48550/arxiv.1905.09703 · pith_short_12: PKFTBC4S47CA · pith_short_16: PKFTBC4S47CAVEGG · pith_short_8: PKFTBC4S

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/PKFTBC4S47CAVEGG232RL5W52U \
  | 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: 7a8b308b92e7c40a90c6d6f515f6ddd51fa719ffc9bb08ed7e0b3087e4f0445d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8242d54f910b72638f54a2d69a1d3481528cf36cc6b2b38b00f33cec846dd24e",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-05-23T15:10:31Z",
    "title_canon_sha256": "7af3afde1157af4741b6955945854a04d75bda8cf0f73ca0e7f3a0737aac3259"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.09703",
    "kind": "arxiv",
    "version": 1
  }
}