Pith Number

pith:AEH4HK46

pith:2007:AEH4HK46XDV4JJKUDNNNTW65TF

not attested not anchored not stored refs pending

Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II

Chiun-Chuan Chen, Horng-Tzer Yau, Robert M. Strain, Tai-Peng Tsai

arxiv:0709.4230 v2 · 2007-09-26 · math.AP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AEH4HK46XDV4JJKUDNNNTW65TF}

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

1 paper in Pith

Global Regularity for Axisymmetric Navier--Stokes Flows with Swirl

Receipt and verification

First computed	2026-07-04T17:24:29.970887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

010fc3ab9eb8ebc4a5541b5ad9dbdd995272006151f30311198610a06a0cc0f1

Aliases

arxiv: 0709.4230 · arxiv_version: 0709.4230v2 · doi: 10.48550/arxiv.0709.4230 · pith_short_12: AEH4HK46XDV4 · pith_short_16: AEH4HK46XDV4JJKU · pith_short_8: AEH4HK46

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/AEH4HK46XDV4JJKUDNNNTW65TF \
  | 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: 010fc3ab9eb8ebc4a5541b5ad9dbdd995272006151f30311198610a06a0cc0f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5983b95b72bcfea76e44e2d0db2db293146a0238b0463ed17a70c89f3ad32cde",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2007-09-26T18:14:12Z",
    "title_canon_sha256": "d5b0e9fb9960e8360898c5ee76a41d0cbba77bce4a4d034bb18dc47b23740b16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.4230",
    "kind": "arxiv",
    "version": 2
  }
}