Pith Number

pith:3ZMNY4MM

pith:2012:3ZMNY4MMOKXHK2X4TKZ56WECGB

not attested not anchored not stored refs pending

Complex Interpolation of Weighted Besov- and Lizorkin-Triebel Spaces (long version)

Jan Vybiral, Leszek Skrzypczak, Winfried Sickel

arxiv:1212.1614 v3 · 2012-12-07 · 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{3ZMNY4MMOKXHK2X4TKZ56WECGB}

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	2026-05-18T02:50:24.465140Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de58dc718c72ae756afc9ab3df588230473958e37cd7cccae7724c85902cef31

Aliases

arxiv: 1212.1614 · arxiv_version: 1212.1614v3 · doi: 10.48550/arxiv.1212.1614 · pith_short_12: 3ZMNY4MMOKXH · pith_short_16: 3ZMNY4MMOKXHK2X4 · pith_short_8: 3ZMNY4MM

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/3ZMNY4MMOKXHK2X4TKZ56WECGB \
  | 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: de58dc718c72ae756afc9ab3df588230473958e37cd7cccae7724c85902cef31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c4585e722537e148f4bd1ba52083afb441df065aac73eef5ab3857649c4c0b4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-12-07T14:16:02Z",
    "title_canon_sha256": "020c4228359a9367532295e6fecc55d97767f5e9ba635c64925bcd34a3ecfe2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.1614",
    "kind": "arxiv",
    "version": 3
  }
}