Pith Number

pith:6WHJTAW4

pith:2024:6WHJTAW4N2J5ESUGAJJ3X5E6NV

not attested not anchored not stored refs pending

On the integrability properties of Leray-Hopf solutions of the Navier-Stokes equations on $\mathbb{R}^3$

Sauli Lindberg

arxiv:2412.13066 v2 · 2024-12-17 · 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{6WHJTAW4N2J5ESUGAJJ3X5E6NV}

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.

Cited by

1 paper in Pith

The 2D Euler equations are well-posed for generic initial data in $L^2$

Receipt and verification

First computed	2026-07-05T09:58:26.898777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f58e9982dc6e93d24a860253bbf49e6d4959935df7b12325a52bac7f811dee4f

Aliases

arxiv: 2412.13066 · arxiv_version: 2412.13066v2 · doi: 10.48550/arxiv.2412.13066 · pith_short_12: 6WHJTAW4N2J5 · pith_short_16: 6WHJTAW4N2J5ESUG · pith_short_8: 6WHJTAW4

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/6WHJTAW4N2J5ESUGAJJ3X5E6NV \
  | 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: f58e9982dc6e93d24a860253bbf49e6d4959935df7b12325a52bac7f811dee4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2823e34f6ddece2ef0fc5d504f2803d18c0d4ad70fb5efd13fea3c370c036410",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-17T16:31:09Z",
    "title_canon_sha256": "b107643c75d3c17aeb20644c7581973cdf8d1dbf30e147b167c357b4f8f1734c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.13066",
    "kind": "arxiv",
    "version": 2
  }
}