Pith Number

pith:WNQM5MMM

pith:2019:WNQM5MMMIGT5YKF6GT4CP6WQQR

not attested not anchored not stored refs pending

Maximal inequalities and exponential estimates for stochastic convolutions driven by L\'{e}vy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations

Jiahui Zhu, Wei Liu, Zdzis{\l}aw Brze\'zniak

arxiv:1907.11867 v1 · 2019-07-27 · math.PR · 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{WNQM5MMMIGT5YKF6GT4CP6WQQR}

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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	2026-05-17T23:39:22.757270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b360ceb18c41a7dc28be34f827fad08463402469fa3a19d7dcd6f0b5f0e0de2c

Aliases

arxiv: 1907.11867 · arxiv_version: 1907.11867v1 · doi: 10.48550/arxiv.1907.11867 · pith_short_12: WNQM5MMMIGT5 · pith_short_16: WNQM5MMMIGT5YKF6 · pith_short_8: WNQM5MMM

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/WNQM5MMMIGT5YKF6GT4CP6WQQR \
  | 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: b360ceb18c41a7dc28be34f827fad08463402469fa3a19d7dcd6f0b5f0e0de2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4f516a98caecce47a19323b6cbd0f8717919ff2cdbb7907d787c46616a1610c",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-07-27T07:35:43Z",
    "title_canon_sha256": "2efc6b0c9a93077e3ca32de4b27ab50081004a08eba51c96220a7d90fce208f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.11867",
    "kind": "arxiv",
    "version": 1
  }
}