Pith Number

pith:GI7DGXRQ

pith:2011:GI7DGXRQL4ROO6XKFETPURRGCM

not attested not anchored not stored refs pending

Characterizations of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces

Amiran Gogatishvili, Pekka Koskela, Yuan Zhou

arxiv:1106.2561 v1 · 2011-06-13 · math.CA · 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{GI7DGXRQL4ROO6XKFETPURRGCM}

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	2026-05-18T04:20:05.412978Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

323e335e305f22e77aea2926fa46261333e8e513e17da1de7bdc1178b2978187

Aliases

arxiv: 1106.2561 · arxiv_version: 1106.2561v1 · doi: 10.48550/arxiv.1106.2561 · pith_short_12: GI7DGXRQL4RO · pith_short_16: GI7DGXRQL4ROO6XK · pith_short_8: GI7DGXRQ

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/GI7DGXRQL4ROO6XKFETPURRGCM \
  | 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: 323e335e305f22e77aea2926fa46261333e8e513e17da1de7bdc1178b2978187

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c45bd778c9a10a1b25dada752789c664b0652bb8f0223f6cd28a5b43368bec3b",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-06-13T20:25:45Z",
    "title_canon_sha256": "c2b84530a7af0b7a46b99afae00f588c4f3779a046c6968fb267a6d17e110981"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.2561",
    "kind": "arxiv",
    "version": 1
  }
}