Pith Number

pith:GKQTONBD

pith:2010:GKQTONBD4GFJVZOMFYNFNLAKXO

not attested not anchored not stored refs pending

Continuous characterizations of Besov-Lizorkin-Triebel spaces and new interpretations as coorbits

Tino Ullrich

arxiv:1007.3418 v2 · 2010-07-20 · 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{GKQTONBD4GFJVZOMFYNFNLAKXO}

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	2026-05-18T04:40:10.187631Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32a1373423e18a9ae5cc2e1a56ac0abba92b8ca00defbf382359e40d2e1c22d3

Aliases

arxiv: 1007.3418 · arxiv_version: 1007.3418v2 · doi: 10.48550/arxiv.1007.3418 · pith_short_12: GKQTONBD4GFJ · pith_short_16: GKQTONBD4GFJVZOM · pith_short_8: GKQTONBD

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/GKQTONBD4GFJVZOMFYNFNLAKXO \
  | 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: 32a1373423e18a9ae5cc2e1a56ac0abba92b8ca00defbf382359e40d2e1c22d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50cc1d82ee87d26e3909f739c7324f30948c86029ce2fe667fc9797c4a293723",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-07-20T13:31:00Z",
    "title_canon_sha256": "d9c74451368265179a1664240c5402e6ba137d770491f7486f5d4d9b809751ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.3418",
    "kind": "arxiv",
    "version": 2
  }
}