Pith Number

pith:OCNXE74J

pith:2012:OCNXE74JE6NIKXIREL7MYTQYHC

not attested not anchored not stored refs pending

The Characterization of Radial Subspaces of Besov- and Lizorkin-Triebel Spaces by Differences

Jan Vybiral, Leszek Skrzypczak, Winfried Sickel

arxiv:1212.2375 v1 · 2012-12-11 · 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{OCNXE74JE6NIKXIREL7MYTQYHC}

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	2026-05-18T03:38:45.100532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

709b727f89279a855d1122fecc4e1838a75dadab560e3c0b6724f2f660b4287e

Aliases

arxiv: 1212.2375 · arxiv_version: 1212.2375v1 · doi: 10.48550/arxiv.1212.2375 · pith_short_12: OCNXE74JE6NI · pith_short_16: OCNXE74JE6NIKXIR · pith_short_8: OCNXE74J

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/OCNXE74JE6NIKXIREL7MYTQYHC \
  | 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: 709b727f89279a855d1122fecc4e1838a75dadab560e3c0b6724f2f660b4287e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ec6cc63e341a761ec7dfa87af61ca07f778167feca9461cfdf5e9322a709781",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-12-11T10:35:12Z",
    "title_canon_sha256": "fbd01eb7c643d8a074c5150b976613db537002802a5cc7ec0db5b45df50851de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2375",
    "kind": "arxiv",
    "version": 1
  }
}