Pith Number

pith:KZN4HGQL

pith:2014:KZN4HGQLEXZM7V7VTTV4AHRUIM

not attested not anchored not stored refs pending

${L^p}$-Liouville Theorems for Invariant Partial Differential Operators in ${\mathbb{R}^n}$

Alessia E. Kogoj, Ermanno Lanconelli

arxiv:1411.5238 v1 · 2014-11-19 · 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{KZN4HGQLEXZM7V7VTTV4AHRUIM}

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	2026-05-18T02:34:44.101060Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

565bc39a0b25f2cfd7f59cebc01e34430b33a5ff26583202afc1d36a58d21430

Aliases

arxiv: 1411.5238 · arxiv_version: 1411.5238v1 · doi: 10.48550/arxiv.1411.5238 · pith_short_12: KZN4HGQLEXZM · pith_short_16: KZN4HGQLEXZM7V7V · pith_short_8: KZN4HGQL

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/KZN4HGQLEXZM7V7VTTV4AHRUIM \
  | 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: 565bc39a0b25f2cfd7f59cebc01e34430b33a5ff26583202afc1d36a58d21430

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80b05f75b709e5372077be4ff98d44192fb5fe556f5108d7a3a992b662821595",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-11-19T14:32:29Z",
    "title_canon_sha256": "89366b5307fc38949566718358424d907b87ff72ebff51f0a78b334765f5edf6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.5238",
    "kind": "arxiv",
    "version": 1
  }
}