Pith Number

pith:AWGHVAO2

pith:2014:AWGHVAO2CFCHUZKUVD3AY6O6XH

not attested not anchored not stored refs pending

A Liouville theorem for $p$-harmonic functions on exterior domains

Daniel Daners, Daniel Hauer, E. N. Dancer

arxiv:1411.4224 v1 · 2014-11-16 · 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{AWGHVAO2CFCHUZKUVD3AY6O6XH}

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	2026-05-18T01:25:18.387255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

058c7a81da11447a6554a8f60c79deb9ee17fd0d080f56cef172e3df5dc0212e

Aliases

arxiv: 1411.4224 · arxiv_version: 1411.4224v1 · doi: 10.48550/arxiv.1411.4224 · pith_short_12: AWGHVAO2CFCH · pith_short_16: AWGHVAO2CFCHUZKU · pith_short_8: AWGHVAO2

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/AWGHVAO2CFCHUZKUVD3AY6O6XH \
  | 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: 058c7a81da11447a6554a8f60c79deb9ee17fd0d080f56cef172e3df5dc0212e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f136c732a422d63a3aa8d1c9a7365d346360bdcf14752cf823803262fd73f98",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-11-16T07:37:42Z",
    "title_canon_sha256": "738586d5f79966698b61923682ec42f706bfeb9c26abe6b0f064417dd292f14b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.4224",
    "kind": "arxiv",
    "version": 1
  }
}