Pith Number

pith:DF45RMUM

pith:2014:DF45RMUMNRRLTFPYFMBWYOTA7O

not attested not anchored not stored refs pending

A Liouville Theorem for the Fractional Laplacian

Ran Zhuo, Wenxiong Chen, Xuewei Cui, Zixia Yuan

arxiv:1401.7402 v1 · 2014-01-29 · 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{DF45RMUMNRRLTFPYFMBWYOTA7O}

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	2026-05-18T03:00:48.600272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1979d8b28c6c62b995f82b036c3a60fb85d9566c82066b660e3efe45a0bbf6fe

Aliases

arxiv: 1401.7402 · arxiv_version: 1401.7402v1 · doi: 10.48550/arxiv.1401.7402 · pith_short_12: DF45RMUMNRRL · pith_short_16: DF45RMUMNRRLTFPY · pith_short_8: DF45RMUM

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/DF45RMUMNRRLTFPYFMBWYOTA7O \
  | 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: 1979d8b28c6c62b995f82b036c3a60fb85d9566c82066b660e3efe45a0bbf6fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72b07e8046843a1d1eeb639d450b0b0924c047114de8c1c33d54bae4bbf71c74",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-01-29T03:23:53Z",
    "title_canon_sha256": "a4f8dc77bfa653b3625d45fd81733ccd176b379688a27036b43679d9469f471a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.7402",
    "kind": "arxiv",
    "version": 1
  }
}