Pith Number

pith:BRTKRH3E

pith:2014:BRTKRH3EVSAYIPOI3PQXTTDO56

not attested not anchored not stored refs pending

Measure density and extension of Besov and Triebel-Lizorkin functions

Heli Tuominen, Lizaveta Ihnatsyeva, Toni Heikkinen

arxiv:1409.0379 v1 · 2014-09-01 · 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{BRTKRH3EVSAYIPOI3PQXTTDO56}

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	2026-05-18T02:43:52.884456Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c66a89f64ac81843dc8dbe179cc6eef8880e17584b5d02d389eb7625f4d0850

Aliases

arxiv: 1409.0379 · arxiv_version: 1409.0379v1 · doi: 10.48550/arxiv.1409.0379 · pith_short_12: BRTKRH3EVSAY · pith_short_16: BRTKRH3EVSAYIPOI · pith_short_8: BRTKRH3E

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/BRTKRH3EVSAYIPOI3PQXTTDO56 \
  | 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: 0c66a89f64ac81843dc8dbe179cc6eef8880e17584b5d02d389eb7625f4d0850

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4693b2dc22faac8de19e2049f4e15eefe48b03c0e1f6cdf23b2dda40b6a640db",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-09-01T12:10:43Z",
    "title_canon_sha256": "aa794dcfbdb732a29c6d400f40a59acc293d7041df1f57a2128ddc9d2ef38b6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.0379",
    "kind": "arxiv",
    "version": 1
  }
}