Pith Number

pith:3VBJG7LT

pith:2018:3VBJG7LTL4NWXDGQI2VC6MEZRN

not attested not anchored not stored refs pending

Liouville theorem and isolated singularity of fractional Laplacian system with critical exponents

Jiguang Bao, Yimei Li

arxiv:1805.06006 v1 · 2018-05-12 · 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{3VBJG7LTL4NWXDGQI2VC6MEZRN}

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	2026-05-18T00:15:49.182990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd42937d735f1b6b8cd046aa2f30998b52ccc009f51f5bdc6139d7b739ecac23

Aliases

arxiv: 1805.06006 · arxiv_version: 1805.06006v1 · doi: 10.48550/arxiv.1805.06006 · pith_short_12: 3VBJG7LTL4NW · pith_short_16: 3VBJG7LTL4NWXDGQ · pith_short_8: 3VBJG7LT

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/3VBJG7LTL4NWXDGQI2VC6MEZRN \
  | 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: dd42937d735f1b6b8cd046aa2f30998b52ccc009f51f5bdc6139d7b739ecac23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ea4d18cbf78c6ab6c440f522d87cb7d769094d3ba59312d9bbe152cffe71fcb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-05-12T13:06:22Z",
    "title_canon_sha256": "1d9be7028206ec56216499f70f88bede552ff83621febadd083ec5759e44eb59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.06006",
    "kind": "arxiv",
    "version": 1
  }
}