Pith Number

pith:KC6XSV3L

pith:2026:KC6XSV3LFZTN75ISA5N4MTNBAM

not attested not anchored not stored refs pending

Liouville theorems for the fractional Navier-Stokes equations with arbitrary asymptotic state at infinity

Changzhi Liu, Wenke Tan

arxiv:2606.31794 v1 · 2026-06-30 · 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{KC6XSV3LFZTN75ISA5N4MTNBAM}

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	2026-07-01T01:18:15.446515Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50bd79576b2e66dff512075bc64da1031e8d79338df24d299c7f8ef9b98c8771

Aliases

arxiv: 2606.31794 · arxiv_version: 2606.31794v1 · doi: 10.48550/arxiv.2606.31794 · pith_short_12: KC6XSV3LFZTN · pith_short_16: KC6XSV3LFZTN75IS · pith_short_8: KC6XSV3L

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/KC6XSV3LFZTN75ISA5N4MTNBAM \
  | 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: 50bd79576b2e66dff512075bc64da1031e8d79338df24d299c7f8ef9b98c8771

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41359efec34d50e54479d65ea2ae06582fb7851e1d84482b5332fdf04a3ed284",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-30T15:12:13Z",
    "title_canon_sha256": "f1da03f0c628781d052996412f34be0fbdc95015314012685576274bf848bf5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31794",
    "kind": "arxiv",
    "version": 1
  }
}