Pith Number

pith:XNOLMMHU

pith:2013:XNOLMMHUJNG3RYY55GMC4DQNWZ

not attested not anchored not stored refs pending

Pointwise and grand maximal function characterizations of Besov-type and Triebel-Lizorkin-type spaces

Tom\'as Soto

arxiv:1304.1587 v2 · 2013-04-05 · 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{XNOLMMHUJNG3RYY55GMC4DQNWZ}

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	2026-05-18T01:35:05.322750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb5cb630f44b4db8e31de9982e0e0db6697aa8734d6203427dca2a0f5280e2ba

Aliases

arxiv: 1304.1587 · arxiv_version: 1304.1587v2 · doi: 10.48550/arxiv.1304.1587 · pith_short_12: XNOLMMHUJNG3 · pith_short_16: XNOLMMHUJNG3RYY5 · pith_short_8: XNOLMMHU

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/XNOLMMHUJNG3RYY55GMC4DQNWZ \
  | 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: bb5cb630f44b4db8e31de9982e0e0db6697aa8734d6203427dca2a0f5280e2ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6ca028011f7ce492ebf92e67551b99ba7b88af2b8e05f65bab1b6d7eeeeafef",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-04-05T00:27:04Z",
    "title_canon_sha256": "006bdfea80c02526d5132d8021bf12bad2657fbc53696c7608f12017946a7208"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.1587",
    "kind": "arxiv",
    "version": 2
  }
}