Pith Number

pith:CK53GKFJ

pith:2023:CK53GKFJKS4XSMAQTXTU4OEU5T

not attested not anchored not stored refs pending

A Liouville theorem in the Heisenberg group

Alberto Roncoroni, Dario D. Monticelli, Giovanni Catino, Yanyan Li

arxiv:2310.10469 v1 · 2023-10-16 · math.AP · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CK53GKFJKS4XSMAQTXTU4OEU5T}

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.

Cited by

1 paper in Pith

Compactness of Solutions to Sub-Elliptic Equations with Potential on the Heisenberg Group

Receipt and verification

First computed	2026-07-05T07:01:20.434224Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12bbb328a954b97930109de74e3894ecd94811b90a51f28c70d6965130cde72a

Aliases

arxiv: 2310.10469 · arxiv_version: 2310.10469v1 · doi: 10.48550/arxiv.2310.10469 · pith_short_12: CK53GKFJKS4X · pith_short_16: CK53GKFJKS4XSMAQ · pith_short_8: CK53GKFJ

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/CK53GKFJKS4XSMAQTXTU4OEU5T \
  | 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: 12bbb328a954b97930109de74e3894ecd94811b90a51f28c70d6965130cde72a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6bb3e91b312f60ef9798d532f33df456388efdcb9c301cc495bad8d4ab2786ec",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2023-10-16T14:49:55Z",
    "title_canon_sha256": "7732e8c6839f9dbae9b48b7ee60c26ea9d092603693fe49476a12c4cbb7eb9f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.10469",
    "kind": "arxiv",
    "version": 1
  }
}