Pith Number

pith:K33FGB5J

pith:2014:K33FGB5JTR5ALWL7DFBE3WGVO7

not attested not anchored not stored refs pending

Trace and extension operators for Besov spaces and Triebel-Lizorkin spaces with variable exponents

Takahiro Noi

arxiv:1410.1185 v1 · 2014-10-05 · 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{K33FGB5JTR5ALWL7DFBE3WGVO7}

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	2026-05-18T02:41:02.531153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56f65307a99c7a05d97f19424dd8d577edc9aad1f7cfe49e15a158ce03e5c1a8

Aliases

arxiv: 1410.1185 · arxiv_version: 1410.1185v1 · doi: 10.48550/arxiv.1410.1185 · pith_short_12: K33FGB5JTR5A · pith_short_16: K33FGB5JTR5ALWL7 · pith_short_8: K33FGB5J

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/K33FGB5JTR5ALWL7DFBE3WGVO7 \
  | 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: 56f65307a99c7a05d97f19424dd8d577edc9aad1f7cfe49e15a158ce03e5c1a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc3b3b0c7cc9a850f34ab3f6dd29c588cce8a55d3362f11caad27a551b3dc9e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-10-05T18:01:47Z",
    "title_canon_sha256": "c0b0d8549339a625f8cbf8861642c7a2bf5fba781f14166e501e84ef2d7edc25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.1185",
    "kind": "arxiv",
    "version": 1
  }
}