Pith Number

pith:VTSB3OKD

pith:2011:VTSB3OKDYTTF2LGV7OXEU7FGZW

not attested not anchored not stored refs pending

Spaces of variable smoothness and integrability: Characterizations by local means and ball means of differences

Henning Kempka, Jan Vybiral

arxiv:1103.5357 v2 · 2011-03-28 · 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{VTSB3OKDYTTF2LGV7OXEU7FGZW}

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	2026-05-18T04:00:38.067821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ace41db943c4e65d2cd5fbae4a7ca6cd9b94ad273976beec7dba2452adfb4275

Aliases

arxiv: 1103.5357 · arxiv_version: 1103.5357v2 · doi: 10.48550/arxiv.1103.5357 · pith_short_12: VTSB3OKDYTTF · pith_short_16: VTSB3OKDYTTF2LGV · pith_short_8: VTSB3OKD

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/VTSB3OKDYTTF2LGV7OXEU7FGZW \
  | 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: ace41db943c4e65d2cd5fbae4a7ca6cd9b94ad273976beec7dba2452adfb4275

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e268d1c47ff740d78503363f1bd648048354b41029bf7a01fe86e0c737e3759a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-03-28T13:59:23Z",
    "title_canon_sha256": "6328f34a7f6c5a2cddf06b6cdb13ed94a2ff2358542d200cbacc425436c9b453"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.5357",
    "kind": "arxiv",
    "version": 2
  }
}