Pith Number

pith:OHIT6GPV

pith:2016:OHIT6GPV6NY3Z43NOFB6LAYFZK

not attested not anchored not stored refs pending

Kato-Ponce inequalities on weighted and variable Lebesgue spaces

David Cruz-Uribe, Virginia Naibo

arxiv:1601.06854 v2 · 2016-01-26 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OHIT6GPV6NY3Z43NOFB6LAYFZK}

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	2026-05-18T01:14:17.434781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71d13f19f5f371bcf36d7143e58305ca9cb77c5715ecf04a722f6d75372edbe2

Aliases

arxiv: 1601.06854 · arxiv_version: 1601.06854v2 · doi: 10.48550/arxiv.1601.06854 · pith_short_12: OHIT6GPV6NY3 · pith_short_16: OHIT6GPV6NY3Z43N · pith_short_8: OHIT6GPV

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/OHIT6GPV6NY3Z43NOFB6LAYFZK \
  | 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: 71d13f19f5f371bcf36d7143e58305ca9cb77c5715ecf04a722f6d75372edbe2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abe2fafa9bc3843a7c87fa2b1629d4c84b7213cf7441e26763609d81322d96e7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-01-26T00:14:11Z",
    "title_canon_sha256": "d18d1aca232b714ef46d390d6946a9e9f6f81843a8ddfbcf3e8bc271b72a1ab2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.06854",
    "kind": "arxiv",
    "version": 2
  }
}