Pith Number

pith:YEF5DK4J

pith:2012:YEF5DK4JUNMY3VZNFZFSZ2W3IC

not attested not anchored not stored refs pending

Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D-domains

El\.zbieta Motyl, Zdzis{\l}aw Brze\'zniak

arxiv:1208.3386 v2 · 2012-08-16 · 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{YEF5DK4JUNMY3VZNFZFSZ2W3IC}

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	2026-05-18T00:53:40.993312Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c10bd1ab89a3598dd72d2e4b2ceadb40914fb34c7cd81638c56f4b3cae1c938e

Aliases

arxiv: 1208.3386 · arxiv_version: 1208.3386v2 · doi: 10.48550/arxiv.1208.3386 · pith_short_12: YEF5DK4JUNMY · pith_short_16: YEF5DK4JUNMY3VZN · pith_short_8: YEF5DK4J

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/YEF5DK4JUNMY3VZNFZFSZ2W3IC \
  | 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: c10bd1ab89a3598dd72d2e4b2ceadb40914fb34c7cd81638c56f4b3cae1c938e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8ed3debc22ddab71c7e20cc96dd41186f5b9afd4a82be57e6fa0ea308f5aed4",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-08-16T14:53:56Z",
    "title_canon_sha256": "d37cb4e0e7b44f817ee62b698d6a88e4a2861dd60747ae1e40ef033136db503e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3386",
    "kind": "arxiv",
    "version": 2
  }
}