Pith Number

pith:WO2FKDJ7

pith:2013:WO2FKDJ7JRQWA734BK4PPEMCLC

not attested not anchored not stored refs pending

Rearrangement invariant optimal range for Hardy type operators

Javier Soria, Pedro Tradacete

arxiv:1311.3582 v1 · 2013-11-14 · math.FA · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WO2FKDJ7JRQWA734BK4PPEMCLC}

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	2026-05-18T03:07:04.430936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3b4550d3f4c61607f7c0ab8f79182588142f0bd79d61a8c2c9f0f7533fc9e20

Aliases

arxiv: 1311.3582 · arxiv_version: 1311.3582v1 · doi: 10.48550/arxiv.1311.3582 · pith_short_12: WO2FKDJ7JRQW · pith_short_16: WO2FKDJ7JRQWA734 · pith_short_8: WO2FKDJ7

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/WO2FKDJ7JRQWA734BK4PPEMCLC \
  | 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: b3b4550d3f4c61607f7c0ab8f79182588142f0bd79d61a8c2c9f0f7533fc9e20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "690dae7666748924613a7becba8297ba0de99ec1a66650421d5c39662bbaea5f",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-11-14T17:08:26Z",
    "title_canon_sha256": "3db0d62af147858afdca5ea36609454cafe9b4549f055191676c7547569b467f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.3582",
    "kind": "arxiv",
    "version": 1
  }
}