Pith Number

pith:PGTGWD4A

pith:2011:PGTGWD4A6ZH26KMG5LTHINUZPF

not attested not anchored not stored refs pending

Local means and atoms in vector-valued function spaces

Benjamin Scharf

arxiv:1103.6159 v1 · 2011-03-31 · 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{PGTGWD4A6ZH26KMG5LTHINUZPF}

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	2026-05-18T04:25:13.874356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79a66b0f80f64faf2986eae67436997955057ac6fda149b1cbee976b69eb1429

Aliases

arxiv: 1103.6159 · arxiv_version: 1103.6159v1 · doi: 10.48550/arxiv.1103.6159 · pith_short_12: PGTGWD4A6ZH2 · pith_short_16: PGTGWD4A6ZH26KMG · pith_short_8: PGTGWD4A

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/PGTGWD4A6ZH26KMG5LTHINUZPF \
  | 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: 79a66b0f80f64faf2986eae67436997955057ac6fda149b1cbee976b69eb1429

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71f96193fa35e4a22b94512736fa305688dd4d11d629f1674c67286bbe019b6f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-03-31T12:45:32Z",
    "title_canon_sha256": "c30b5eaed52425dbbfe432010b5bd545d2fd317ed650e8b5015e2f1e7adbb05d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.6159",
    "kind": "arxiv",
    "version": 1
  }
}