Pith Number

pith:LNG67QDX

pith:2026:LNG67QDXKQVIB3DNW2GFHKKS4L

not attested not anchored not stored refs pending

Global solutions to the Navier--Stokes equations with large vertical velocities in $\dot{B}_{\infty,\sigma}^{-1}(\mathbb{R}^3)$

Mikihiro Fujii

arxiv:2607.04918 v1 · 2026-07-06 · 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{LNG67QDXKQVIB3DNW2GFHKKS4L}

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	2026-07-07T02:20:12.728261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b4defc077542a80ec6db68c53a952e2ce79f9a777c0e9bd9062d5acb97b83d0

Aliases

arxiv: 2607.04918 · arxiv_version: 2607.04918v1 · doi: 10.48550/arxiv.2607.04918 · pith_short_12: LNG67QDXKQVI · pith_short_16: LNG67QDXKQVIB3DN · pith_short_8: LNG67QDX

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/LNG67QDXKQVIB3DNW2GFHKKS4L \
  | 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: 5b4defc077542a80ec6db68c53a952e2ce79f9a777c0e9bd9062d5acb97b83d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04c916515d2d604382c7cb431e0fbd47b77b9812ddc753c6f0c856dbe2e3a8a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-06T10:48:11Z",
    "title_canon_sha256": "4c205b7b29d7bdbe9ffa083fb8bc7dfd1e9045f701ae8a6bfd620fe1e08400d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.04918",
    "kind": "arxiv",
    "version": 1
  }
}