Pith Number

pith:5ENQG6DU

pith:2017:5ENQG6DUWL7WCLLFS7XLCRUUKD

not attested not anchored not stored refs pending

Smoothing Properties of Bilinear Operators and Leibniz-Type Rules in Lebesgue and Mixed Lebesgue Spaces

Jarod Hart, Rodolfo H. Torres, Xinfeng Wu

arxiv:1701.02631 v1 · 2017-01-10 · 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{5ENQG6DUWL7WCLLFS7XLCRUUKD}

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	2026-05-18T00:53:03.798777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e91b037874b2ff612d6597eeb1469450d3bc70bc9853cadbe5ab457617c36995

Aliases

arxiv: 1701.02631 · arxiv_version: 1701.02631v1 · doi: 10.48550/arxiv.1701.02631 · pith_short_12: 5ENQG6DUWL7W · pith_short_16: 5ENQG6DUWL7WCLLF · pith_short_8: 5ENQG6DU

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/5ENQG6DUWL7WCLLFS7XLCRUUKD \
  | 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: e91b037874b2ff612d6597eeb1469450d3bc70bc9853cadbe5ab457617c36995

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa8f4bdf139ad37ca55b1fedb40f1e5f164f5a8f6813562aa6ad5e602b0fb65f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-01-10T15:18:11Z",
    "title_canon_sha256": "fee445cb9aeca54b4840d458ca40db258a3b991bd40bccf5e72105a0f5f294ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.02631",
    "kind": "arxiv",
    "version": 1
  }
}