Pith Number

pith:UNGRKTRX

pith:2018:UNGRKTRXOABJSEXJOVMRJ5U57R

not attested not anchored not stored refs pending

The Liouville theorem for $p$-harmonic functions and quasiminimizers with finite energy

Anders Bj\"orn, Jana Bj\"orn, Nageswari Shanmugalingam

arxiv:1809.07155 v1 · 2018-09-19 · math.MG · math.AP

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\usepackage{pith}
\pithnumber{UNGRKTRXOABJSEXJOVMRJ5U57R}

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Record completeness

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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

Bounded geometry and $p$-harmonic functions under uniformization and hyperbolization

Receipt and verification

First computed	2026-07-05T02:10:16.046907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a34d154e3770029912e9755914f69dfc52d3947df7d83e37bd4ebede710c0f64

Aliases

arxiv: 1809.07155 · arxiv_version: 1809.07155v1 · doi: 10.48550/arxiv.1809.07155 · pith_short_12: UNGRKTRXOABJ · pith_short_16: UNGRKTRXOABJSEXJ · pith_short_8: UNGRKTRX

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/UNGRKTRXOABJSEXJOVMRJ5U57R \
  | 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: a34d154e3770029912e9755914f69dfc52d3947df7d83e37bd4ebede710c0f64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c1baa4276e12c2603a12758fd7110bac2ff38f59a7637055cb7cd9cef26067c",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2018-09-19T12:48:38Z",
    "title_canon_sha256": "cdf2cf4a7f450bc00ebb64eb234383d5aa9845fc302fc84ebbbfc73708f04893"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.07155",
    "kind": "arxiv",
    "version": 1
  }
}