Pith Number

pith:7PDOR5XH

pith:2016:7PDOR5XH2TQAKNHUTVYO3UTJ3H

not attested not anchored not stored refs pending

Liouville property for $f$-harmonic functions with polynomial growth

Jia-Yong Wu

arxiv:1610.03923 v3 · 2016-10-13 · math.DG · 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{7PDOR5XH2TQAKNHUTVYO3UTJ3H}

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	2026-05-17T23:59:26.673016Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbc6e8f6e7d4e00534f49d70edd269d9e0b5f591bf4a9ee4739fe3aa25bf1610

Aliases

arxiv: 1610.03923 · arxiv_version: 1610.03923v3 · doi: 10.48550/arxiv.1610.03923 · pith_short_12: 7PDOR5XH2TQA · pith_short_16: 7PDOR5XH2TQAKNHU · pith_short_8: 7PDOR5XH

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/7PDOR5XH2TQAKNHUTVYO3UTJ3H \
  | 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: fbc6e8f6e7d4e00534f49d70edd269d9e0b5f591bf4a9ee4739fe3aa25bf1610

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f1cdcc5e5685e2142930ac784383418820a4cd3eb56ff9b2700e779c2fe7e40",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-10-13T03:21:26Z",
    "title_canon_sha256": "9a2b647d1bf147c4ede7b4ac7db2a40645c979113b87eeab47b87c08353ab4e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.03923",
    "kind": "arxiv",
    "version": 3
  }
}