Pith Number

pith:QV6YC2UO

pith:2026:QV6YC2UOC3LPTGWEFR3ARIPR7F

not attested not anchored not stored refs pending

New decay estimates and Liouville type theorems for the 3D axisymmetric stationary Navier-Stokes equations

Guoxu Yang, Wendong Wang

arxiv:2608.06040 v1 · 2026-08-06 · 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{QV6YC2UOC3LPTGWEFR3ARIPR7F}

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	2026-08-07T00:55:09.760196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

857d816a8e16d6f99ac42c7608a1f1f96b2ea7db8c313add0d113a389bce0618

Aliases

arxiv: 2608.06040 · arxiv_version: 2608.06040v1 · doi: 10.48550/arxiv.2608.06040 · pith_short_12: QV6YC2UOC3LP · pith_short_16: QV6YC2UOC3LPTGWE · pith_short_8: QV6YC2UO

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/QV6YC2UOC3LPTGWEFR3ARIPR7F \
  | 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: 857d816a8e16d6f99ac42c7608a1f1f96b2ea7db8c313add0d113a389bce0618

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77536df6f01868a27c946b7344ac62318d71e8e30d9b3e1243bc49a9706b8cd5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-06T13:49:30Z",
    "title_canon_sha256": "155132d7694528aa4834d656a85f6163e8edb4b69fefbef2aead48f9aefaf50e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.06040",
    "kind": "arxiv",
    "version": 1
  }
}