Pith Number

pith:5CKN5QED

pith:2023:5CKN5QEDLGUXLCS26BCBTQUW43

not attested not anchored not stored refs pending

Liouville type theorems for subelliptic systems on the Heisenberg group with general nonlinearity

Michael Ruzhansky, Rong Zhang, Vishvesh Kumar

arxiv:2303.04210 v1 · 2023-03-07 · 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{5CKN5QEDLGUXLCS26BCBTQUW43}

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	2026-07-05T05:49:05.336217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e894dec08359a9758a5af04419c296e6e26b175e76b0a7500015e115c0c1d67b

Aliases

arxiv: 2303.04210 · arxiv_version: 2303.04210v1 · doi: 10.48550/arxiv.2303.04210 · pith_short_12: 5CKN5QEDLGUX · pith_short_16: 5CKN5QEDLGUXLCS2 · pith_short_8: 5CKN5QED

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/5CKN5QEDLGUXLCS26BCBTQUW43 \
  | 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: e894dec08359a9758a5af04419c296e6e26b175e76b0a7500015e115c0c1d67b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fcc5dd9530c9f0f0a0d0bf13dd3b8c6315a1891b64afce03398ea8914c3f4de",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2023-03-07T20:01:18Z",
    "title_canon_sha256": "09dbb3a4fabd750cceb3f462395910108ca1b56c65172ed5db8956fc67b0e99d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.04210",
    "kind": "arxiv",
    "version": 1
  }
}