Pith Number

pith:KCSHRDTF

pith:2019:KCSHRDTFK7QBMDI3GXNGKOBU2A

not attested not anchored not stored refs pending

The Navier--Stokes equations in exterior Lipschitz domains: $\mathrm{L}^p$-theory

Keiichi Watanabe, Patrick Tolksdorf

arxiv:1906.02713 v1 · 2019-06-06 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KCSHRDTFK7QBMDI3GXNGKOBU2A}

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	2026-05-17T23:44:00.394799Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50a4788e6557e0160d1b35da653834d03fa1c0d07a3a66b4fe29487fffd9c342

Aliases

arxiv: 1906.02713 · arxiv_version: 1906.02713v1 · doi: 10.48550/arxiv.1906.02713 · pith_short_12: KCSHRDTFK7QB · pith_short_16: KCSHRDTFK7QBMDI3 · pith_short_8: KCSHRDTF

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/KCSHRDTFK7QBMDI3GXNGKOBU2A \
  | 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: 50a4788e6557e0160d1b35da653834d03fa1c0d07a3a66b4fe29487fffd9c342

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55eff8e3faeb1bd2664520f0a6d66da885010418fb878007d9330744789c5589",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-06-06T17:30:28Z",
    "title_canon_sha256": "37e2534e77623b267d35cce2fa45feb3185f8e19a9a56a399c9633fd958aa5b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.02713",
    "kind": "arxiv",
    "version": 1
  }
}