Pith Number

pith:W2R35SGA

pith:2024:W2R35SGAH7WWXTMIQHQXCLJX62

not attested not anchored not stored refs pending

Sharp non-uniqueness for the Navier-Stokes equations in R^3

Changxing Miao, Weikui Ye, Yao Nie

arxiv:2412.09637 v1 · 2024-12-06 · 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{W2R35SGAH7WWXTMIQHQXCLJX62}

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

2 papers in Pith

Non-Uniqueness for Nonlinear Fokker--Planck Equations and Their Associated Distribution-Dependent SDEs

Sharp non-uniqueness of weak solutions to 2D magnetohydrodynamic equations

Receipt and verification

First computed	2026-07-05T09:48:39.291391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6a3bec8c03fed6bcd8881e1712d37f6935823b1f04b7d8f5d1b062fc81d59aa

Aliases

arxiv: 2412.09637 · arxiv_version: 2412.09637v1 · doi: 10.48550/arxiv.2412.09637 · pith_short_12: W2R35SGAH7WW · pith_short_16: W2R35SGAH7WWXTMI · pith_short_8: W2R35SGA

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/W2R35SGAH7WWXTMIQHQXCLJX62 \
  | 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: b6a3bec8c03fed6bcd8881e1712d37f6935823b1f04b7d8f5d1b062fc81d59aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef5fe1baf2aa9a23dbf000e851ddff824a05c8f34f126f52630de859746c840a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-06T12:21:18Z",
    "title_canon_sha256": "9fa2cac6ad931040b5fc5c31b83b3dae54ede2ecddf738f0375079261d48fc6d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.09637",
    "kind": "arxiv",
    "version": 1
  }
}