Pith Number

pith:5JLKJOD5

pith:2016:5JLKJOD5XZCVDFIYQGEJINCUAR

not attested not anchored not stored refs pending

Ill-posedness for the 3D inhomogeneous Navier-Stokes equations in the critical Besov space near $L^6$ framework

Renhui Wan

arxiv:1609.04551 v3 · 2016-09-15 · 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{5JLKJOD5XZCVDFIYQGEJINCUAR}

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	2026-05-18T00:33:02.374446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea56a4b87dbe45519518818894345404585b34c55a8ba8dfe3eb5f9e503dcb82

Aliases

arxiv: 1609.04551 · arxiv_version: 1609.04551v3 · doi: 10.48550/arxiv.1609.04551 · pith_short_12: 5JLKJOD5XZCV · pith_short_16: 5JLKJOD5XZCVDFIY · pith_short_8: 5JLKJOD5

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/5JLKJOD5XZCVDFIYQGEJINCUAR \
  | 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: ea56a4b87dbe45519518818894345404585b34c55a8ba8dfe3eb5f9e503dcb82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68aff212abf77e3648a48358ab15a1869e57a3c04a32ed7d54e6f4413840dbea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-15T09:42:30Z",
    "title_canon_sha256": "a1fbf9ce885171e591a5ab0b00f6f12d3cb97f3f3bf212462b523632ce9c39ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.04551",
    "kind": "arxiv",
    "version": 3
  }
}