Pith Number

pith:23MWB2DX

pith:2013:23MWB2DXHIEG45TZE22E5PASJL

not attested not anchored not stored refs pending

Parabolic Littlewood-Paley inequality for $\phi(-\Delta)$-type operators and applications to Stochastic integro-differential equations

Ildoo Kim, Kyeong-Hun Kim, Panki Kim

arxiv:1302.5053 v1 · 2013-02-20 · math.FA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{23MWB2DXHIEG45TZE22E5PASJL}

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	2026-05-18T03:33:00.313623Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6d960e8773a086e767926b44ebc124ad563b27e6652b8267e5d39273a1552aa

Aliases

arxiv: 1302.5053 · arxiv_version: 1302.5053v1 · doi: 10.48550/arxiv.1302.5053 · pith_short_12: 23MWB2DXHIEG · pith_short_16: 23MWB2DXHIEG45TZ · pith_short_8: 23MWB2DX

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/23MWB2DXHIEG45TZE22E5PASJL \
  | 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: d6d960e8773a086e767926b44ebc124ad563b27e6652b8267e5d39273a1552aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbf967204dc086571a7982f476ca0ef69b4912f78af8852c5851d07a3e7f633c",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-02-20T18:01:49Z",
    "title_canon_sha256": "552125f64beea231badd216aca6e663cd65527b74c6cc5103cb8a3c9b8deec28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.5053",
    "kind": "arxiv",
    "version": 1
  }
}