Pith Number

pith:5IU4QMJQ

pith:2015:5IU4QMJQNSK6FOZVT2JKGFJA2V

not attested not anchored not stored refs pending

Criticality of the Axially Symmetric Navier-Stokes Equations

Qi S. Zhang, Zhen Lei

arxiv:1505.02628 v2 · 2015-05-11 · 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{5IU4QMJQNSK6FOZVT2JKGFJA2V}

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

Large-Data Global Regularity for Three-Dimensional Navier--Stokes I: A Direct First-Threshold Continuation Proof for the Axisymmetric Swirl Class

Receipt and verification

First computed	2026-05-18T02:00:58.434959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea29c831306c95e2bb359e92a31520d55648ae59e4b2750ac12a5baef35c5b85

Aliases

arxiv: 1505.02628 · arxiv_version: 1505.02628v2 · doi: 10.48550/arxiv.1505.02628 · pith_short_12: 5IU4QMJQNSK6 · pith_short_16: 5IU4QMJQNSK6FOZV · pith_short_8: 5IU4QMJQ

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/5IU4QMJQNSK6FOZVT2JKGFJA2V \
  | 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: ea29c831306c95e2bb359e92a31520d55648ae59e4b2750ac12a5baef35c5b85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86a5b60edc2a81bcfd539e607b96d275fa976dc95fe12b0332df3bcf67f6aa33",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-05-11T14:06:47Z",
    "title_canon_sha256": "c8e09d157b597da8771cd1d2730818c865f3aed8050afb076b56f868616224c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.02628",
    "kind": "arxiv",
    "version": 2
  }
}