Pith Number

pith:B5MODR3N

pith:2015:B5MODR3NXIXPKIZFF5BQBENIO3

not attested not anchored not stored refs pending

Characterizations of Besov and Triebel-Lizorkin Spaces via Averages on Balls

Amiran Gogatishvili, Dachun Yang, Feng Dai, Wen Yuan

arxiv:1507.08004 v1 · 2015-07-29 · 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{B5MODR3NXIXPKIZFF5BQBENIO3}

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	2026-05-18T01:36:08.668730Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f58e1c76dba2ef523252f430091a876fff27bcca2710a9516737bccccda971f

Aliases

arxiv: 1507.08004 · arxiv_version: 1507.08004v1 · doi: 10.48550/arxiv.1507.08004 · pith_short_12: B5MODR3NXIXP · pith_short_16: B5MODR3NXIXPKIZF · pith_short_8: B5MODR3N

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/B5MODR3NXIXPKIZFF5BQBENIO3 \
  | 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: 0f58e1c76dba2ef523252f430091a876fff27bcca2710a9516737bccccda971f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af0a912c53a85efb18ec48d055b6263c40755f57a062924fd56f2f6f17be3295",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-07-29T01:38:46Z",
    "title_canon_sha256": "a25c5e76923144bc3684eb06e0b78a266e9f1d047a6c588f5bbcd15967526ce8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08004",
    "kind": "arxiv",
    "version": 1
  }
}