Pith Number

pith:62NEVINQ

pith:2008:62NEVINQEA72ZZV5QU4JK4YCEM

not attested not anchored not stored refs pending

Liouville Theorem for Dunkl Polyharmonic Functions

Guangbin Ren, Liang Liu

arxiv:0811.0962 v1 · 2008-11-06 · math.CA · 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{62NEVINQEA72ZZV5QU4JK4YCEM}

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	2026-07-04T15:15:51.481658Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f69a4aa1b0203face6bd8538957302232bf2daaa8b3434cfaa329f3d3cc9b676

Aliases

arxiv: 0811.0962 · arxiv_version: 0811.0962v1 · doi: 10.48550/arxiv.0811.0962 · pith_short_12: 62NEVINQEA72 · pith_short_16: 62NEVINQEA72ZZV5 · pith_short_8: 62NEVINQ

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/62NEVINQEA72ZZV5QU4JK4YCEM \
  | 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: f69a4aa1b0203face6bd8538957302232bf2daaa8b3434cfaa329f3d3cc9b676

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd71d5fa4e1e9d989cf04b4d50f6a0be679ef2439a27e5f195950f67fac7f6f2",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2008-11-06T15:03:58Z",
    "title_canon_sha256": "61e9889c3791af5493c632ab7760bb5341d9536877f7f603c278959c201e0c4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.0962",
    "kind": "arxiv",
    "version": 1
  }
}