Pith Number

pith:5BODWL3B

pith:2026:5BODWL3BK5VVY63FNTU4UYKZ53

not attested not anchored not stored refs pending

Liouville Theorem for $(p,q)$-Laplace Equations

Hua Zhu, Yang Zhou

arxiv:2606.20033 v1 · 2026-06-18 · 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{5BODWL3BK5VVY63FNTU4UYKZ53}

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	2026-06-19T16:13:01.209702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e85c3b2f61576b5c7b656ce9ca6159eed5352bf22bf589f0132ff2ca7da1dd65

Aliases

arxiv: 2606.20033 · arxiv_version: 2606.20033v1 · doi: 10.48550/arxiv.2606.20033 · pith_short_12: 5BODWL3BK5VV · pith_short_16: 5BODWL3BK5VVY63F · pith_short_8: 5BODWL3B

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/5BODWL3BK5VVY63FNTU4UYKZ53 \
  | 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: e85c3b2f61576b5c7b656ce9ca6159eed5352bf22bf589f0132ff2ca7da1dd65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dbb4aa2294d602025c57ebaf9e89de6cb2af28cb3c8fc078fb686684e2ccfce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-18T10:06:35Z",
    "title_canon_sha256": "bb3909f5d84650ac7200804b851e2de1bc7c76bc7f6e9236e5b20149dd179450"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20033",
    "kind": "arxiv",
    "version": 1
  }
}