Pith Number

pith:IJTNR7JE

pith:2026:IJTNR7JE6ML7INU6UVT6I3CRAO

not attested not anchored not stored refs pending

Critical mass threshold for the 2D Patlak-Keller-Segel-Navier-Stokes system

Dongyi Wei, Wendong Wang, Zhifei Zhang

arxiv:2606.02070 v1 · 2026-06-01 · 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{IJTNR7JE6ML7INU6UVT6I3CRAO}

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	2026-06-02T02:05:05.074743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4266d8fd24f317f4369ea567e46c5103b0a62a5171e69f32e82bb567595f9c00

Aliases

arxiv: 2606.02070 · arxiv_version: 2606.02070v1 · doi: 10.48550/arxiv.2606.02070 · pith_short_12: IJTNR7JE6ML7 · pith_short_16: IJTNR7JE6ML7INU6 · pith_short_8: IJTNR7JE

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/IJTNR7JE6ML7INU6UVT6I3CRAO \
  | 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: 4266d8fd24f317f4369ea567e46c5103b0a62a5171e69f32e82bb567595f9c00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8f070212ab61be32f09385c1e30849582a01a67c2aa6dbca86d98643b490be4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-01T10:59:56Z",
    "title_canon_sha256": "0c53f11acdd85c2fe36ce9a7cf3fc5afe968dba0e11bad4379800fa14872333c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.02070",
    "kind": "arxiv",
    "version": 1
  }
}