Pith Number

pith:GZ6IJBSC

pith:2011:GZ6IJBSCL7GG6TIDVA5GLHYGG3

not attested not anchored not stored refs pending

An integral representation for Besov and Lipschitz spaces

Kehe Zhu

arxiv:1101.2995 v1 · 2011-01-15 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GZ6IJBSCL7GG6TIDVA5GLHYGG3}

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	2026-05-17T23:53:19.507937Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

367c8486425fcc6f4d03a83a659f0636de66d1681f568126e102f2ddce9da4e4

Aliases

arxiv: 1101.2995 · arxiv_version: 1101.2995v1 · doi: 10.48550/arxiv.1101.2995 · pith_short_12: GZ6IJBSCL7GG · pith_short_16: GZ6IJBSCL7GG6TID · pith_short_8: GZ6IJBSC

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/GZ6IJBSCL7GG6TIDVA5GLHYGG3 \
  | 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: 367c8486425fcc6f4d03a83a659f0636de66d1681f568126e102f2ddce9da4e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3156908f46defcb00fffec8f39258b34f6cc1c68596380720641441518bcefba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2011-01-15T16:00:50Z",
    "title_canon_sha256": "59a5f9d290e93f0e9d0bc527bdda541a053ddba88b1cbac0df102091b2cf9a9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2995",
    "kind": "arxiv",
    "version": 1
  }
}