Pith Number

pith:TRHK3EF4

pith:2026:TRHK3EF4LBC6CZ3G3ECJJLHBZX

not attested not anchored not stored refs pending

Liouville-type theorems for the stationary fractional Navier-Stokes equations in $\mathbb{R}^n$

Jihoon Lee, Juhyeong Lee

arxiv:2606.28959 v1 · 2026-06-27 · 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{TRHK3EF4LBC6CZ3G3ECJJLHBZX}

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	2026-06-30T01:17:47.212849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c4ead90bc5845e16766d90494ace1cddec0edcfb241ea06b7daa4878703a88f

Aliases

arxiv: 2606.28959 · arxiv_version: 2606.28959v1 · doi: 10.48550/arxiv.2606.28959 · pith_short_12: TRHK3EF4LBC6 · pith_short_16: TRHK3EF4LBC6CZ3G · pith_short_8: TRHK3EF4

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/TRHK3EF4LBC6CZ3G3ECJJLHBZX \
  | 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: 9c4ead90bc5845e16766d90494ace1cddec0edcfb241ea06b7daa4878703a88f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bec5f0a3fdc712075dcb29c604da8fd9c547080b8765be53b4b3cc6da8b89d5a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-27T15:00:06Z",
    "title_canon_sha256": "6b62bae4b40d42ec6b42e11896c0d52b68bd59d8b4c4e609bc5c642f66704043"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28959",
    "kind": "arxiv",
    "version": 1
  }
}